What Is the Difference between an American and European Style Option in the Context of Token Lock-Ups?

The distinction lies in the exercise date. A European style option can only be exercised on its expiration date.

An American style option, conversely, can be exercised at any time up to and including its expiration date. This is relevant to token lock-ups if the lock-up is structured as an option; an American style lock-up would allow early access, while a European style lock-up would strictly enforce the release date.