As far as I'm aware they're just distributed, identical versions of the same database (except during updates).
The're been little consistency in how a dance has progressed. The update hasn't always started on the same data center.
www, www2, and www3 can show the results from any data centre. During an update, www flips between updated centers and centers with the old info. www2 and 3 have the new info before it's made fully public.
The different data centers are actually not absolutelly identical.
They are very close. But SERPS and specially the numbers for the total pages found differ slightly. Even if they all run the same Google update Version. Safari and its "open in tabs" feature can be a very nice 'homegrown dance tool' when you feed it with the datacenters and a query that you care about.
These slight differences have probably many reasons. One would be the constant updates that go into the datacenters gradually. The other one might be the nature of googles concept of having many many redundant machines doing the same job. Systems and their data go offline all the time. The google-engine deals with that very gracefully. Searches always work. Just that minor details get shifted.
Another thing to note is that a datacenter itself seems to get its results from different clusters: During an update the result of a DC may 'flicker'.
Same principle as with the DNS mapping of www.google.com to the different datacenters. Just behind the actual webserver, and therefor only observable. You can not know which cluster is beeing used, if you query www-xy.google.com.
I am guessing here. But my observations go nicely along with these theories.