I confess I was getting confused about what ArcGIS Online is and how it differed from ArcGIS.com. I'm so glad I asked Bernie Szukalski to explain it. Here's how to think about it: Like Microsoft's Office Live (which I confess I do not use, but I know what it is)!
When you are in PowerPoint (which I also don't use) and connect to Office Live you get presented with content for PowerPoint - PPT templates, graphics, etc. When you go there from Excel you get spreadsheet templates and other Excel goodies. Based on "how you get there" the repository (because that's what it is really) offers different content.
ArcGIS Online is the same way. if you visit from ArcGIS desktop you see ArcGIS desktop stuff (layer packages say). If you visit from ArcGIS Explorer Desktop you see content it can use. You can visit ArcGIS Online via the ArcGIS.com website (to poke around or manage groups, etc.). You can also use ArcGIS.com to access one of ArcGIS Online's Web clients (the Map Viewer, ArcGIS Explorer Online).
So, ArcGIS Online isn't a website, it's more of a repository hosted in the cloud, that you can visit via a number of different clients (some browser-based, some not). It holds all kinds of goodies for those clients: data services, task services, templates...
It really is the center of the "new" Esri universe. It's taking the reigns from the former center of that universe: ArcGIS for Desktop.