*just an assistant ESL teacher
They are often used interchangeably (they are synonyms).
But, uncover often involves taking off some type of cover. This can be something like a blanket, dirt, or even taking off the cover of lies to uncover the truth about something.
Find out is often, but not always, something we do on purpose. If I don't know something I will look it up to find out (but not to discover it).
I can discover or find out (or realize or notice) something about myself but I don't think I can uncover something about myself.
- For Teachers