A paradox is a logical puzzle that seems to contradict itself. No it isn't. Actually, it is. An oxymoron is a figure of speech — words that seem to cancel each other out, like "working vacation" or "instant classic."
A paradox makes your brain hurt because it seems like something is true and false at the same time. M.C. Escher's "Relativity" is a visual paradox. The floor is the ceiling! Part of the fun of a paradox is figuring out if it really is one. How about this one: A father and son get in a car wreck and the father dies. The son goes to the hospital, but the doctor says, "I can't operate on him. He's my son." Confused? Ha! Not a paradox, though — the doctor is his mom. Here's a paradox by William Wordsworth, "The child is father of the man." Check out the word in action:
"He seemed to absorb the baffling paradoxes of quantum theory with ease." (Big Science)
"The answer, for Muji, is a neat paradox, like a Zen koan: massive minimalism through perpetual growth." (New Yorker)
Oh jumbo shrimp of the world, we're not calling you morons. You're oxymorons! The word itself is an oxymoron, a contradiction. It comes from the Greek oxys for "sharp" and moros for "stupid." Sharply stupid. Oxymorons gone mild wild:
"This article proves that good economic news is an oxymoron." (New York Times)
"The ultimate oxymoron: I was once invited to an agoraphobic convention," he said. (Washington Post)
Both are contradictions, but a paradox is something to think on, and an oxymoron is a description, enjoyed in the moment then gone.