Yeah, you could argue that choosing C is just choosing a particular subset of C++.
The main difference from choosing a different subset, e.g. “Google C++” (i.e. writing C++ according to the Google style guide), is that the compiler enforces that you stick to the subset.
C's string handling is so abominably terrible that sometimes all people really need is "C with std::string".
Oh, and smart pointers too.
And hash maps.
Vectors too while we're at it.
I think that's it.
C is not a subset of C++, there are some subtle things you can do in C that are not valid C++