Both are independent networks. Cdma2000 specification was developed by the Third Generation Partnership Project 2 (3GPP2), a partnership consisting of five telecommunications standards bodies: ARIB and TTC in Japan, CWTS in China, TTA in Korea and TIA in North America. Cdma2000 has already been implemented to several networks as an evolutionary step from cdmaOne as cdma2000 provides full backward compatibility with IS-95B. Cdma2000 is not constrained to only the IMT-2000 band, but operators can also overlay acdma2000 1x system, which supports 144 kbps now and data rates up to 307 kbps in the future, on top of their existing cdmaOne network.
UMTS was developed mainly for countries with GSM networks, because these countries have agreed to free new frequency ranges for UMTS networks. Because it is a new technology and in a new frequency band, whole new radio access network has to be build. The advantage is that new frequency range gives plenty of new capacity for operators. 3GPP is overseeing the standard development and has wisely kept the core network as close to GSM core network as possible. UMTS phones are not meant to be backward compatible with GSM systems. (but subscriptions (=SIM card) can be, and dual mode phone will solve the compatibility problems, hopefully). UMTS also has 2 flavors FDD (will be implemented first) and TDD.