The answer is (a) - a problem is cooked when there's an unintended solution (called a cook). If the intended solution fails, the problem's fault is simply "no solution". These are the two main types of unsound problems.
What is a cooked problem?
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When is a chess problem cooked?
If the problem is:
"White to move and win"
then when is the problem described as "cooked":
a) The poser of the problem intended one key move which allows White to win - but there is another White move that also wins, unforeseen by poser of the problem?
b) White does NOT win, because the poser of the problem did not foresee a Black countermove that saves the position for Black?