Yep, C++ is a superset of C langauge, not vice versa
After C, there came a language called C+, which was very soon replaced by C++, the ++ added to C, is actually the increment operator which is available in the C language. So, C++ in a way meant the next incremental version of C.
The basic structure of both the language remains the same, even Java follows the same basic syntax.
The main difference between C and C++ was ofcourse the Object-Oriented part :P