The UCLA Library Catalog is everything held (i.e. bought, licensed, subscribed to, acquired as gifts) by UCLA, as well as materials that are freely available to the general public. These materials include books, journals, magazines, DVDs and videos, manuscripts, microfilm, databases, and so on.
The Melvyl Catalog is everything held by University of California libraries, including UCLA. So pretty much everything in the UCLA Catalog is in the Melvyl Catalog.
OCLC's WorldCat has catalog records from libraries worldwide. Not every library everywhere, but from any libraries that have given their records to OCLC. Pretty much everything in the UCLA Library Catalog and the University of California system's Melvyl Catalog should show up in WorldCat.
The University of California has partnered with OCLC to launch a pilot project to see if all three catalogs can be accessed from a single user interface. The catalog is called Next Generation Melvyl and has nifty features not available in any of the other catalogs, but it's beta, so there are still bugs to be worked out. You can help us work out some of those bugs by clicking the feedback link located at the bottom of each page in Next Gen Melvyl and tell us what you think.