UML is a graphical modeling language which can be used to depict different issues about a project/system. It can be used to foster communication in a team, regardless of the used process. RUP is a process framework, giving you a huge amount of practices you can pick from to build your own software development process. Many of those practices make use of UML, including, but not restricted to, the elaboration phase. Did that help?
The soul is dyed the color of its thoughts. Think only on those things that are in line with your principles and can bear the light of day. The content of your character is your choice. Day by day, what you do is who you become. Your integrity is your destiny - it is the light that guides your way. - Heraclitus