Every level has three stars, and all three are independent of each other. None of them stands in front of the next level.
Three goals
Path. Finish the level. That is all. How many moves it took, how often you undid, how often you were caught — none of it matters.
Master. Finish in the minimum number of moves. That number is not set by hand — it is the length of the shortest solution the game's own solver found. The counter measures your final, uncaught chain of moves; undos do not count, so you can find par by experimenting.
Trace. Collect the level's relic. Relics usually sit off the shortest path, which means in most levels you cannot take Master and Trace in the same run.
Why Master is this hard
On purpose. The Master star is the game's reason to come back; if it were easy it would not be doing its job.
Its difficulty has a measured boundary: for every level, the number of distinct solutions at minimum length was counted. Nine levels have exactly one — but all nine of those are small boards. So there is no level anywhere that is a single needle in a large haystack.
And looking for Master costs nothing: undo is unlimited and free, hints are free, and neither takes a star away.
Why Trace pulls you off the path
Because a relic is a story object. They are the things the caravan leader's sibling left behind along the way — a comb, a whistle, an evil-eye bead. As you collect them the story gallery opens, and they decide which version of the ending you see.
The details are on Setting and tone.
Why none of them lock anything
The game's core promise is that nothing blocks your progress. Getting stuck on a level does not mean you cannot finish the game, and neither does playing imperfectly. The stars are there for people who want them and invisible to people who just want to move on.
The wider version of this is on There is no losing.