What is a paradox and what is Catch 22?

A paradox is basically a statement that is the direct opposite of a statement that could be true.

Catch 22, in my on words, is like hoping that an unreal goal or a goal that is hardly capable of being achieved would come true. For instance, a person may want to go out on a date by a certain time, but they have so many things to do between the time they have set which makes the goal unreal.