When I look up the term "stab" in Wikipedia it says: "In music, a stab is a single staccato note or chord that adds dramatic punctuation to a composition."
So I was wondering, are stab and staccato synonyms?
No. "Staccato" is a more general term than "stab."
A stab usually describes an accented note surrounded by rests. Stabs are often used in film scores to add drama and highlight individual actions. An example would be the famous show scene from the film "Psycho." Each stab of the knife is accompanied by an orchestral stab. (This example is unique because it includes a long string of stabs, they are usually more isolated).
Staccato literally means "separated," though it is usually interpreted by performers as simply "short." It doesn't have the implication of necessarily being loud or dramatic. For instance, an orchestra member might be asked to play a soft, continuous line of staccato eighth notes as an accompaniment line; these notes would not be described as stabs.
I want to clarify something that the current answers haven't yet addressed: staccato doesn't mean short.
Rather, staccato means "separated" or "detached." Albeit rare, you can have a staccato whole note; this won't be a short pitch, but it will be separated from the succeeding pitch.
Staccato pitches can be stabs, but they don't have to be stabs. As such, the two terms are not completely synonymous.