When you ‘discover’ something, you find something that had already existed. Perhaps it was hidden, and therefore, couldn’t be seen. You are not creating anything new, you are merely finding something that was already there.
For example, America existed long before Columbus discovered it in 1492. Similarly, if you discover treasure under your garage, you are finding something that had already been there for some time. But the discovery is something ‘new’ for you. You were not aware of its existence before your discovery. Others, however, may have been aware of it. You may intentionally set out to discover something or you may discover something quite accidentally.
‘Invention’, on the other hand, suggests the creation of something new, something which did not exist before.
For example, Thomas Edison invented the electric light bulb — nothing like it had existed before his invention. It was not new just for the inventor, but for everyone.

The explorers discovered gold deep inside the cave.
I want to invent a machine which will enable people to lose weight in five minutes.