User blog comment:Dragonjet/KanColle Command Center/@comment-175.140.47.229-20140625081722/@comment-1820055-20140627125050

Quick Play

This only shows up when you have a saved API link. This means the extension remembers the last link you've played, and can re-open it anytime. In answering your question, there's actually no difference, since quick play uses API links as mentioned.

Forget this API link

The other button in the Command Center, is actually to forget/delete the API link, and you'll need to re-login to DMM to be able to play again.