I think it's safe to say some moves are objectively better than other moves. Some moves are objectively bad or losing. Some moves are objectively the fastest way to a forced win or forced gain of material. The syntax of "incorrect move" or "wrong" that you have a problem with is just a convenient way of saying "you didn't make the best move in this situation." A common shortcut in the English language.
Of course, I've seen problems where it's not as clear cut as whether one move is objectively better than the other, however, it seems as though in at least 9 out of 10 of these puzzles (so to speak) it's pretty clear.
There are many sites where the viewer is asked to solve a chess puzzle and such and is told to drag the pieces to solve it. In most of these cases, if you try to drag a piece other than the one the programmer wants you to move, you are given the message, "Incorrect move!"
No legal move in chess can be incorrect! If it was, there would be no games played! It's all a matter of opinion!
This really irritates me! The programmer is not the final arbiter of what legal moves are correct and what moves are not. The player is!
frankxhalliwell@gmail.com