With cloud computing you lease virtual servers to host YOUR software. It doesn't have to be web services, you could run DNS or host NFS servers, or your own custom Unix daemons (or WIndows Services) to do whatever you want. If you're a developer you can use it to host svn, trac, and build server. Unlike a colo it's a virtual machine instance. In a cloud you install all your stuff on an instance, then take a snapshot. You can then automatically spin up additional instances in response to load, according to your metrics of load. So if you build the right tools you could have a build server that scales dynamically - more checkins could spin up more instances to run more builds in parallel. When you lease storage you can have it shared across your instances.
Clearly, with EC2, one of the most installed software is mysql. You run it in one or more instances and put the db on S3. With Amazon offering mysql as SaaS you no longer have to deal with provisioning and sizing - it adapts to your usage. I think it sounds like a brilliant time saver and my company will take a close look at it for sure. (We run a lot of backend infrastructure on EC3.)
With SaaS you lease services not servers. Like collaboration tools, web hosting, etc. You don't know what the provider runs the software on - and don't care. You pay for the use of their software, not your own. I get the impression Amazon didn't want to get involved with SaaS for various reasons previously. (There are others who sell SaaS that's hosted on EC2, perhaps Amazon didn't want to compete with their own customers.)