They are not completely different. Entire large projects can be written in C that also compile with a C++ compiler, and it is entirely practical, even easy, to maintain them that way.

My TXR language is like that:

   ./configure cc=g++
   make && make tests

The Lua people have done this too, and call this dialect "Clean C", I think.

Compiles cleanly and tests pass. I usually work with it with a C compiler. Before releases I run it through the C++ compiler to see what breaks, and fix it. (Usually very little and often nothing at all.)

Teaching them at the same time? I'm not sure I would take programming newbies and try to teach them how to program in C such that it also means the same thing as C++. That is to say, I would be confident that I could teach this in a straightforward way; however, the problem would be the lack of supporting material. For instance, there is no reference manual for the "Clean C" language; what would we use as a text book?

One approach would be just to use C resources, and cover the C and C++ differences as one chapter of the course: basically, how to port C programs to the C++ dialect.

I'd definitely teach the students how to leverage the stricter C++ type conversions while keeping the code C, including the following trick:

  #ifdef __cplusplus
  #define strip_qual(TYPE, EXPR) (const_cast<TYPE>(EXPR))
  #define convert(TYPE, EXPR) (static_cast<TYPE>(EXPR))
  #define coerce(TYPE, EXPR) (reinterpret_cast<TYPE>(EXPR))
  #else
  #define strip_qual(TYPE, EXPR) ((TYPE) (EXPR))
  #define convert(TYPE, EXPR) ((TYPE) (EXPR))
  #define coerce(TYPE, EXPR) ((TYPE) (EXPR))
  #endif

This would be a nice way to cover the preprocessor.