The short answer: Either one is what you are looking for, but my first choice would be memcache (the first one you listed), purely based on its correct use of nomenclature.
Now here's how I came to that conclusion:
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.
In summary, both are functionally the same, but they simply have different authors, and the one is simply named more appropriately than the other.
# memcached -u memcached -d -m 30 -l 127.0.0.1 -p 11211
You'll notice there is "-l 127.0.0.1" in your command line. This tells memcached to only listen on the lo interface. If you want to access it from a remote machine, you need to remove this part of the command line.
Best Answer
Elasticsearch is a search and index kind of database, build and optimized for searching and analytics, not for caching.
For a caching server you would use Memcached. But these days there are other alternatives such as Redis (Key-Value database) which is much faster and supports more complex solutions. Carl Zulauf did a great job describing the differences between Redis and Memcached already here on stackoverflow.