>I have heard that in C++ a char is always 1 byte
Yes. Or to be more specific, "char" and "byte" are synonymous terms, and sizeof(char) is guaranteed to be 1.

>and an integer is always 4 bytes on any machine
Nope. The size of an integer is at least 16 bits, but it can be whatever the implementation chooses as long as the basic requirements for type relations are met.

>its weird that 1 byte can still be 1 byte even if
>the type consists of 16 bits instead of 8 @_@.
It's not weird at all when you understand that "byte" is an abstraction for the smallest addressable unit. An octet (the 8-bit entity you're familiar with) is one such concrete implementation of this abstraction.

>I wanted to see if there was some header or implementation
>that defined the way bytes were mapped for each type
The closest you can get is looking in <limits.h>. CHAR_BIT will tell you how many bits are in a byte, and the *MIN/*MAX values will give you an idea of how other types are structured on your system. You can find out the minimum requirements by looking at a suitable draft of the C standard. Example.