They both have the same meaning, while can't is just a contraction of cannot (just like I am and I'm, etc.). Generally, the rule is is that contractions are less formal (in this case can't), while full words are used more formally (in this case cannot). I can't go to the park today (informal) I cannot go to the park today (more formal)

Can't is informal while cannot is formal but they mean the same thing.

"can't" is the short form of "cannot"

They are interchangeable. You can use either in any situation