Opera Mini is sort of half a browser. The page content is pre-rendered on the Opera Mini servers before being sent to your device to be displayed. Opera for Android is a full browser (based on Chromium) and as such does not require pre-rendering on an external server, though Opera does include a compressing proxy named Turbo if you want to reduce your bandwidth usage.
I don't use Mini, but I am told there are some website features it does not support which the full Opera does.