Sharepoint
Sharepoint is a server-based application accessible via the user's browser. It is a major player in the collaboration field, with all the bells and whistles you would expect. Unfortunately it can also come with a pretty high learning curve - mostly on the administrative, rather than user, side.
While very large companies will want to host their own Sharepoint server, medium and small businesses will use a hosted solution like Apptix. Their plans range from $40/mo for up to 50 users and 150MB storage to $100/mo for unlimited users and 500MB storage. An advantage of using a hosted service is the ability to scale up and down as needed - difficult and expensive if you are hosting it yourself.
Groove
I like to think of Groove as Sharepoint's little brother. Groove is, in its most basic form, a P2P (peer-to-peer) application - files are copied and stored on each team member's own computer. This is fine if users are online at the same time so their documents can be updated. However, if team members rarely work shared hours, files would never get update.
That is where the Groove server comes in. With the higher levels of Groove, any document changes, forum discussions or other shared information is shared with a server. Each team member's application checks the server when connected to the internet and updates the documents on the individual computer.
Groove possesses pretty good synchronization logic as well, necessary for when team members change documents when offline.
Groove is currently in Beta and will ship with some versions of Microsoft Office 2007 this Fall (?Winter?).
