This is primarily to collect thoughts into one spot, because I’ve been chatting about this more than just here, lately, and I keep seeing people define these words their own ways and insist that those meanings are what’s generally meant, but folks’ definitions do not align. So let’s look into some dictionaries and etymology and other references. I’ll probably update this with more as I go, but I'm starting with the glossary.

Why am I doing this? Because the arguments I see on the topic usually engage in conflation, equivocation, and circular reasoning, particularly on the issue of “Should Christians spank their children?” This occurs regardless a person’s stance.

I am digging into the words and more in order to separate what is necessarily inherent vs. what nuances, parts, or aspects of meaning must be derived from context, presuppositions, and/or cultural bias. As a side effect, this should find the roots that lead to the divergent interpretations and applications, thereby uncovering the areas where the words get redefined to always refer to Someone Else, but the intent is to identify where assumptions are made in the arguments.

Glossary:

to spank (v.)
Online Etymology Dictionary: “1727, ’to strike forcefully with the open hand, especially on the buttocks,’ possibly imitative of the sound of spanking”
Oxford Dictionary: “Slap with one’s open hand or a flat object, especially on the buttocks as a punishment”
Merriam Webster Dictionary: “to strike especially on the buttocks with the open hand”
American Heritage Dictionary: “To slap on the buttocks with a flat object or with the open hand, as for punishment”
Note: As shown, the word spank generally includes forcefulness as part of the definition. This invalidates the idea that spanking necessarily doesn’t inflict pain and is more about getting the child’s attention or making clear how displeased you are. Individual persons might use spanking in such a manner, but that is an individual usage and not the general reality.
to beat (v.)
Online Etymology Dictionary: “Old English beatan "inflict blows on, thrash" (class VII strong verb; past tense beot, past participle beaten), from Proto-Germanic *bautan (source also of Old Norse bauta, Old High German bozan "to beat"), from PIE root *bhau- "to strike" (see batter (v.)). Of the heart, c. 1200, from notion of it striking against the breast. Meaning "to overcome in a contest" is from 1610s (the source of the sense of "legally avoid, escape" in beat the charges, etc., attested from c. 1920 in underworld slang).”
Oxford Dictionary: “Strike (a person or an animal) repeatedly and violently so as to hurt or injure them, typically with an implement such as a club or whip”
Merriam Webster Dictionary: “to hit (someone) repeatedly in order to cause pain or injury”
American Heritage Dictionary: 1. “To strike repeatedly.” 2. “To subject to repeated beatings or physical abuse; batter.” 3. “To punish by hitting or whipping; flog.”
Note: The fact that beating someone has the express goal of inflicting harm or pain is directly pertinent in the discussion.
consequence (n.)
Online Etymology Dictionary: “late 14c., ’inference, conclusion,’ from Old French consequence ’result’ (13c., Modern French conséquence), from Latin consequentia, from consequentem (nominative consequens), present participle of consequi ’to follow after,’ from com- ’with’ (see com-) + sequi ’to follow’ (see sequel). Sense of ’importance’ (c. 1600) is from notion of being ’pregnant with consequences.’”
Oxford Dictionary: “A result or effect, typically one that is unwelcome or unpleasant”
Merriam Webster Dictionary: “something produced by a cause or necessarily following from a set of conditions”
American Heritage Dictionary: 1. “Something that logically or naturally follows from an action or condition. See Synonyms at effect”; 2. “A punishment or negative repercussion”
Note: It is only the most proscriptive of the dictionaries that makes consequence potentially synonymous with punishment, though all define consequence in such a way that punishment is a type of consequence.
punishment (n.)
Online Etymology Dictionary: “late 14c., from Anglo-French punisement (late 13c.), Old French punissement, from punir (see punish). Meaning ’rough handling’ is from 1811.”
Oxford Dictionary: “The infliction or imposition of a penalty as retribution for an offence”
Merriam Webster Dictionary: “the act of punishing”, “mak[ing] (someone) suffer for a crime or for bad behavior”
American Heritage Dictionary: “The imposition of a penalty or deprivation for wrongdoing”
Note: Therefore, in order for something to be punishment, it must be an action taken to inflict a penalty for an offense. A punishment is a consequence that is a penalty imposed for a violation (ex. you wrecked your car, so you now have points on your license and limitations on your ability to drive). Consequences that would occur regardless (ex. you no longer have a vehicle because you totaled your car) are not punishment.
Note to self: draw Venn diagram
chastisement (n.)
Online Etymology Dictionary: “c. 1300, from chastise + -ment”, chastise being “c. 1300, chastisen, from Old French chastiier ’to warn, advise, instruct; chastise, admonish; punish; dominate, tame’ (12c., Modern French châtier), from Latin castigare ’to set or keep right, to reprove, chasten, to punish,’ literally ’to make pure’ (see castigate). Or perhaps from Middle English chastien (see chasten) + -ise, though this would be early for such a native formation. The form of the modern word ’is not easily accounted for’ [OED].”
Oxford Dictionary: see chastise”, which is 1. “Rebuke or reprimand severely” or 2. “(dated) Punish, especially by beating”
Merriam Webster Dictionary: the act of “criticiz[ing] (someone) harshly for doing something wrong”
American Heritage Dictionary: 1. the act of “punish[ing], as for wrongdoing”; 2. the act of “criticiz[ing] severely; reprimand[ing] or rebuk[ing]”; 3. the act of “purify”-ing something
Note: The word chastisement therefore has an overall meaning and focus on verbal rebuke/reproof, particularly in modern usage, though originally it could reference domination and taming and could sometimes refer to physical punishment. Insofar as Biblical use is concerned, Christians are told to love others and serve or train them, not dominate or tame them, so defining “chastisement” as “domination and taming” would cause Scripture to conflict with Scripture and can therefore be safely disregarded. Further looking into the usage of chastise under Oxford Dictionary indicates that the definition I mark as “2” is actually referencing the “dominate/tame” definition, since it’s used in regards to whips with servants and slaves. That conclusion will warrant more investigation if it proves pertinent, but regardless, the root and majority of definitions of the word does specifically reference various types of verbal response to an unwise action.
discipline (n.)
Online Etymology Dictionary: “early 13c., ’penitential chastisement; punishment,’ from Old French descepline (11c.) ’discipline, physical punishment; teaching; suffering; martyrdom,’ and directly from Latin disciplina ’instruction given, teaching, learning, knowledge,’ also ’object of instruction, knowledge, science, military discipline,’ from discipulus (see disciple (n.)). Sense of ’treatment that corrects or punishes’ is from notion of ’order necessary for instruction.’ The Latin word is glossed in Old English by þeodscipe. Meaning ’branch of instruction or education’ is first recorded late 14c. Meaning ’military training’ is from late 15c.; that of ’orderly conduct as a result of training’ is from c. 1500.”
Oxford Dictionary: “The practice of training people to obey rules or a code of behaviour, using punishment to correct disobedience”; “The controlled behaviour resulting from such training”; “Activity that provides mental or physical training”; “A system of rules of conduct”
Merriam Webster Dictionary: 1. “training that corrects, molds, or perfects the mental faculties or moral character”; 2. “control gained by enforcing obedience or order”; 3. “orderly or prescribed conduct or pattern of behavior”; 4. “a rule or system of rules governing conduct or activity”
American Heritage Dictionary: 1. “Training expected to produce a specific character or pattern of behavior, especially training that produces moral or mental improvement”; 2. “Punishment intended to correct or train”
Note: This makes the word discipline the physical counterpart to verbal chastisement. It’s also focused on what should be done done more than it is on what shouldn’t be done, which puts paid the common application that penalizes a person for what they did wrong without directing to what they should’ve done instead. (Note that even martyrdom happens due to a focus on what should be rather than what shouldn’t—people don’t exactly become martyrs by accepting the status quo.)

Biblical Terms on the Topic:

παιδϵύω (paideuó)
In New Testament: Luke 23:1622; Acts 7:22; Acts 22:3; 1 Corinthians 11:32; 2 Corinthians 6:9; 1 Timothy 1:20; 2 Timothy 2:25; Titus 2:12; Hebrews 12:6710; Revelation 3:19
In Old Testament (in Septuagint / LXX): Leviticus 26:2328; Deuteronomy 4:36; Deuteronomy 8:5; Deuteronomy 21:18; Deuteronomy 22:18; Deuteronomy 32:10; II Samuel 22:48; I Kings 12:1114; II Chronicles 10:1114; Esther 2:7; Psalms 2:10; Psalms 6:1; Psalms 16:7; Psalms 38:1; Psalms 39:11; Psalms 90:10; 10Psalms 94:12; Psalms 105:22; Psalms 118:18; Psalms 141:5; Proverbs 3:12; Proverbs 5:13; Proverbs 9:7; Proverbs 10:4; Proverbs 13:24; Proverbs 19:18; Proverbs 22:3; Proverbs 23:13; Proverbs 28:17; Proverbs 29:1719; Proverbs 31:1; Isaiah 28:26; Isaiah 46:3; Jeremiah 2:19; Jeremiah 6:8; Jeremiah 10:24; Jeremiah 31:18; Jeremiah 46:28; Ezekiel 23:48; Ezekiel 28:3; Hosea 7:1214; Hosea 10:10
BibleHub: “to train children” is identified as the classical Greek meaning and is universally consistent on this source. Instruction, correction, teaching, training, and chastisement are also applied as meanings. A pertinent note is that paideuó is derived from the Greek word for child (pais), and it’s the root of the English words pedagogue and pedagogy.
Greek Word Study Tool: generally “to train/teach/educate”, or to display good training or breeding; the meaning “to chastise or punish” looks to stem solely from New Testament interpretation
Note: The Bible verses will need to be examined individually to see if the classical definition could apply to all or if the definition “to punish” is a necessary addition.
TBC

Temporary items to be aides in further investigation:

OpenBible.info
discipline
chastise
chastisement
child discipline
topics
distinction(s) between discipline and chastisement issued by parent to child vs. punishment issued by government to wrongdoer
in what manner (if any) Christ’s suffering and death, as applicable to the "sword" of the government, is pertinent to child rearing