Handbooks use these interchangeably as often as they distinguish them, and when they do distinguish, they disagree about how. Any source stating the difference with total confidence is reporting one tradition as though it were the only one.
Side by side
Aspect
Apophasis
Paralipsis
Core sense
Speaking by denying
Passing over
Agreed distinction
No
No
Used as synonyms
Frequently
Frequently
Effect
Identical
Identical
What each one means
Apophasis
Saying something by declaring that you will not say it — I won't mention his convictions, I'm not going to bring up what happened last year. In theology the same word names something quite different: negative theology, approaching God only through what he is not.