I am curious. Can you give a concrete example or two? Also, if not about a board game, where else would this apply?
pure instruction -> teaching through playing -> friendly match -> competitive match
Let's use a card game as an example.
Pure instruction: Both players play with their cards visible to each other, and the teacher coaches rules and strategy as they play.
Teaching through playing: The hands are now private, but the teacher will tell the student if they're making bad moves and allow do-overs. The teacher may also set up situations for the student to take advantage of.
Friendly match: The teacher is playing against the student. No coaching is given. But, nit-picky procedural rules are not always followed. (You've set that card down and your hand left it, you can't pick it up again).
Competitive match: Rules are followed to the letter.
Think of a chess game, for example. We can play by the rules to the letter, but if I decide to systematically take your pieces one-by-one or "forget" some of my own experience to perhaps make it more fun, are elements I assumed are in the original comment above.
Essentially anything where "I've consumed more calories that you have" or "I've had more years to think that you have" are an unfair advantage for purposes of fun.