The comment you're replying to described it as three choices, but you can also consider it a spectrum.

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.