In hindsight the key difference is that a group text only goes to that specific group of people that you have already established relationships with and have some idea who they all are, whereas with Twitter it was there the beginning of the cultural shift, due to reality shows and other factors, of publicizing one's private life.
and it turned out that at least in the beginning when the internet wasn't quite as full of garbage as it is now, that broadcasting yourself to a bunch of people you do know plus a much larger circle of people they know but whom you do not know, ended up bringing a net positive return of new contacts to you. This was and still is incredibly helpful especially for young people just starting out in life who need to build up networks (of all ... kinds) very quickly.
The limited space available in a tweet ensured that everyone was capped at the same minimal level of effort, so there was little or no expectation that you had to put a lot of work or thought or polish into what you were saying - rawness and immediacy were prioritized over polish. Quantity finally had a slight edge over quality, because everything was tinged with the quality of "novelty" at the time.