UMTS defines a collection of protocols and standards which make up the 3G network. The protocol part of UMTS is W-CDMA, this is the technology which defines how the signals travel through the air, between the device and the base stations. MAP, or Mobile Application Part, is an existing part of GSM; it’s the protocol that allows the actual phone to be used, such as routing the calls to and from the mobile subscriber, this runs at the core of the 3G network. Then you have things such as the speech codec’s, which are standards which define how your voice, or audio, is sampled, and digitised, so it can be sent over the network, these are also from the 2G network, such as AMR and EFR.
Although UMTS is the term which covers all of the protocols and standards that make up the 3G networks, W-CDMA is almost always used to describe 3G networks, as it is the term that describes the air interface. WCDMA networks are UMTS, FOMA, and J-Phone.