It's so weird how it works. I think they just want the best material gain, unless there in an obvious checkmate.
Is there always only 1 correct move?
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It's a meta-rule (stratagem) for solvers and most of them start using it once they are aware of it. It is most useful where you solve by elimination. As per Sherlock Holmes: “When you have eliminated the impossible, whatever remains, however improbable, must be the truth”. When you can reject 2 out of 3 serious candidate moves, the one remaining must be correct.
However the rated puzzles are not completely consistent in it. Commonly your mission is to win, and there is always 1 move which wins considerably easier than the others. This changes when mate is nearby. You are expected to execute a mate in 1 even when a mate in 2 or a queen win is equally simple and effective. Suddenly your mission has then changed from "winning" to "handing out the fastest checkmate".
In the rated puzzles is there always only 1 correct move at each step?
It would be possible to devise puzzles with only one correct final position but maybe more than 1 way to get there.
Sometimes you can see the position you need to get to to solve the puzzle but there might at first seem as if there is more than 1 intermediate step to get there. I have always found that if you analyse the puzzle there will actually only be 1 correct intermediate step sequence.
Just curious if that is a rule that can be relied on when solving rated puzzles or whether sometimes there actually can be more than 1 intermediate step?