(PartlyStolen from ServerFault)
I think that both are functionally the same, but they simply have different authors, and the one is simply named more appropriately than the other.
Here is a quick backgrounder in naming conventions (for those unfamiliar), which explains the frustration by the question asker: For many *nix applications, the piece that does the backend work is called a "daemon" (think "service" in Windows-land), while the interface or client application is what you use to control or access the daemon. The daemon is most often named the same as the client, with the letter "d" appended to it. For example "imap" would be a client that connects to the "imapd" daemon.
This naming convention is clearly being adhered to by memcache when you read the introduction to the memcache module (notice the distinction between memcache and memcached in this excerpt):
Memcache module provides handy
  procedural and object oriented
  interface to memcached, highly
  effective caching daemon, which was
  especially designed to decrease
  database load in dynamic web
  applications.
The Memcache module also provides a
  session handler (memcache).
More information about memcached can
  be found at »
  http://www.danga.com/memcached/.
The frustration here is caused by the author of the PHP extension which was badly named memcached, since it shares the same name as the actual daemon called memcached. Notice also that in the introduction to memcached (the php module), it makes mention of libmemcached, which is the shared library (or API) that is used by the module to access the memcached daemon:
memcached is a high-performance,
  distributed memory object caching
  system, generic in nature, but
  intended for use in speeding up
  dynamic web applications by
  alleviating database load.
This extension uses libmemcached
  library to provide API for
  communicating with memcached servers.
  It also provides a session handler
  (memcached).
Information about libmemcached can be
  found at »
  http://tangent.org/552/libmemcached.html.