The biggest difference has to do with how Twitter has been used. Your retweets and likes show up on your profile and thus edits made to tweets may change what appears when someone looks at your profile. Unless they do it in some smarter way than most[0], this could personally devastating to folks because likes and retweets are viewed as endorsements (despite what some think).

The second biggest difference is newspapers tend not to change the entire point of the article in their edits, and aren't out to troll their engaged audience.

0: ie show the edited content on the page alongside the previous version(s) with the same prominence and, most importantly, without having to click anything to show an old version.

ETA: typos.