What makes Twitter fundamentally different from other messaging applications (and with that, similar to blogging) is that it is subscription based. Unlike with e-mail, who the readers of the message are is not determined by you, but by the readers themselves. Only people subscribed to (or visiting) your blog or Twitter account will read a message. That's also why you don't receive spam on Twitter or your feed reader, if you do that's because you voluntarily subscribed to a feed containing spam. All you have to do to get rid of it is unsubscribe.
Twitter is very simple currently, but I think either Twitter or soon-to-come Twitter clones will add functionality that opens a lot of new opportunity and will make it more than just a toy. The first thing is the ability to address individuals. This is already possible in Twitter to some extent through the Jabber and SMS text interface I think. You send Twitter "d username message" and message will be sent to only username. As I discussed before this opens a whole world of opportunity. Twitter, and this is important, only allows this if username is a friend or 'follower' of you, i.e. if username is subscribed to your messages. My guess is that soon it will be possible to create groups of users that you can address together. All of the people in your group will have to be friends or followers of course.
With this subscription-based model you create an essentially spam-free messaging platform.
It would get even more interesting if you can send individuals or groups special kinds of messages. Polls for example. Sometimes I want to have dinner with some friends. How I currently arrange this is by sending them an e-mail asking when they are available and where they want to go. I then collect this data and decide on a date and place, or if necessary send another e-mail with a more limited set of options asking for their opinion again. This is not very practical. There are some services that automate this process a bit more, but it is something that I would like to have in a messenger. So beyond normal text messages there could be other types of messages, such as date picker messages, poll messages and you can probably come up with others.
Twitter messages, like IMs and e-mail have no context. It is not defined whether a message is a response to another message, sometimes this can be deduced from the order in which they appear or their content, but this makes discussions on Twitter pretty much impossible to follow. Therefore I think it would be nice if Twitter would keep track of which message is a reply to which. Public discussions and discussions within groups will be much easier as they can be displayed in a threaded structure.
Just a rather unstructured numbers ideas of where this new Twitter thing could head.
(I wrote and published this post from Google Docs, to see how that works.)