Yes, until recently I thought so too. But on reflection I have decided that this description is really only an assessment of the (superficially similar but actually quite different) old Facebook Status.
What makes a Tweet different from a Facebook Status (as was) is that, while one (the latter) is a "thinking aloud monologue" which others might or might not care to tune in to, the other is one part of a group dialogue where you are actively addressing your tuned-in audience.
With Facebook Status, you might answer the question "What are you doing now?" with such banalities as how much you are enjoying the sunny weather or looking forward to a concert on the weekend. People may or may not care - it's not addressed to anyone in particular.
But with Twitter, you might actively point friends to an article you just read that you think they should read too, or indicate where you will be this evening at what time so they can meet you there.
They look superficially similar and, in theory at least, can each be used to mimic the other. No doubt some people will continue to use Twitter in the same empty narcissistic way they used Facebook Status. But in contrast with the former Facebook feature, Twitter is about actively having a conversation, not simply jotting down thoughts in an open diary.