In one way, not a lot. In another way, lots.
The big difference comes with the philosophy behind the language, C++ is an object oriented language. C is a procedural langues, and not intended as an object oriented language (although it can technically be hammered into something that resembles object orientation).
C++ is based on C, which means most C code can be compiled as C++, but "proper" C++ can not be compiled in a C compiler.
To understand more of the differences, you probably need a better understanding of at least ONE of the languages.
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Mats