Listening to an episode of The Philosopher's Zone this morning, The Sorites Paradox. I haven't listened to the whole episode yet but was struck by the guest Dominic Hyde's explanation of what a paradox is.

All paradoxes are characterised by the following general set of features: that we proceed by apparently valid reasoning, that is, apparently good reasoning, from apparently true assumptions to an apparently absurd conclusion.

This shed a lot of light for me, as I had previously believed that for a paradox to properly be a paradox it must be self-contradictory. But with the definition given here then perhaps I was mistaken about ideas such as the Twin Paradox being misnamed as paradoxes.