A byte is CHAR_BIT bits, where CHAR_BIT is required to be at least 8 (and is exactly 8 for the vast majority of implementations).
The word "byte" is commonly used to mean exactly 8 bits, but C and C++ don't define it that way. If you want to refer to exactly 8 bits without ambiguity, that's an "octet".
I think you worded this pretty well. One thing I'd add (and that annoys me about C & C++) is that the size guarantees for integral types boil down to is that CHAR_BIT = sizeof(char) and that sizeof(char) <= sizeof(short) <= sizeof(int) <= sizeof(long). sizeof(T*) (for any T) is not even defined well, and can be OS/compiler specific. Makes cross-platform 32/64-bit support painful, especially because there were no strictly sized integer types before C11 & C++11. Although C11 & C++11 define types like int32_t and int64_t, they're not actually required to be those sizes! The various x-bit types only have to at least be large enough to store x-bits. So, on a hypothetical 40-bit CPU, sizeof(int32_t) could vary well be 40-bits, if that's the natural "word" size for the CPU.
The devil is always in the details, and the devil is very, very annoying...
