Paidia and ludus
Also said as Free play and structured play, Play and game
Two ends of one scale, named by Roger Caillois. Paidia is free, made-up play, with no rules to speak of. Ludus is play bound by rules and goals, made harder on purpose.
It stops the argument about whether something "counts" as a game. Most good games sit somewhere along the scale, and knowing where you want yours saves you from adding scores to a thing that needed none.
Say it
“Open with paidia. Give them five minutes of painting the town with no objectives. Only then introduce the first quest, and never lock the paintbrush away.”
Where you’ve seen it
Minecraft holds both at once: Creative mode is close to pure paidia, with free blocks and no danger, and speedrunning its Survival mode to the Ender Dragon is about as ludic as play can be.
Not to be confused with toy versus game
Paidia and ludus describe how a person is playing. Toy and game describe the thing they are playing with. You can play freely with a chess set by building towers from the pieces.