Xtext is a framework for development of programming languages and domain specific languages. It covers all aspects of a complete language infrastructure, from parsers, over linker, compiler or interpreter to fully-blown top-notch Eclipse IDE integration. It comes with good defaults for all these aspects and at the same time every single aspect can be tailored to your needs.
Xbase is a partial programming language implemented in Xtext and is meant to be embedded and extended within other programming languages and domain-specific languages (DSL) written in Xtext. Xbase is not a new programming language! It’s the basis for a plethora of new programming languages and domain-specific languages.