In broad terms, the C++ language is essentially C with a whole bunch of object oriented stuff added. Nearly all the code you could write in C will also compile and run just fine in C++.
However, there are a few corners of the languages where there are differences. The number of these have been slowly growing over time, but the languages aren't changing rapidly enough for that to be a significant problem.
If you only learn C++, then yes, you will eventually learn almost all aspects of the C language too. If you become expert in C++, then you will be able to identify and understand the places where small differences between the similar parts of C and C++ exist.