Question about running memcached on multiple servers

I have memcached running on two boxes and memcache-client installed and
am ready to integrate into my Rails app.

I see lots of references to running the memcached server daemon process
on several servers. This implies that you would have completely
different caches on each machine, correct? So you would just fire up as
many cache processes as you need to cache different items in hopes of
distributing the load.

There isn't any notion of some sort of distributed cache (cache that
lives on multiple servers), right? That would seem to imply some sort
of replication or cache server affinity.

Right... from the memcache page...