Question: Are RUP and UML related?
The answer is not so simple as the question. RUP is a process (Rational Unified Process). UML is a language (completely independent of process). The RUP does suggest that artifacts are created using UML for your design (although I have seen nowhere where it says this is mandatory, artifacts however of one kind are mandatory). RUP is also a software package in a sense as it comes with templates etc for the design process. Since it is a Rational product it is also integrated with Rational
Rose (their UML design tool). So the answer is if you are using RUP then you will most likely be using UML.