Where to find documentation for definitions for AVR programming in C
When you program in C, you are using a compiler and library provided by someone. The two most common ones are avr-libc https://www.nongnu.org/avr-libc/user-manual/modules.html and Atmel studio https://www.microchip.com/en-us/development-tools-tools-and-software/gcc-compilers-avr-and-arm.
The documentation there should be what you are looking for. For the most part, registers follow the naming convention on the datasheet, but functions need some explanation.