Paradox is a situation or statement which seems difficult to understand because it contains two opposite facts or characteristics.
Example: "This statement is false." If you think it's true, then it must be false, but if you think it's false, it must be true. Now, that's a paradox!
"I always lie" is a paradox because if it is true it must be false
when something is the complete opposite of something else or very different from something else, so that one of them must be wrong
Example: You say that you're good friends and yet you don't trust him. Isn't that a bit of a contradiction?