SPI library on STM32F401

tardishead:
Firstly why would it behave differently? I presumed that any Library functions programmed in Arduino would be recognised by any Arduino compatible board. Why would the function change from setSCK to setSCLK. And would setSCLK work?

That's not a good assumption. Those types of functions are platform-specific. And, in fact, they are not support on some platforms.

"beginTransaction" is not highlighted in red as it is when on Teensy board
as well as "SPI.transfer16". Are these functions still going to work as intended?
Should I be using an SPI library that has been updated for STM32F boards?

Does it compile error-free? If so, there's a good chance it will work. The definitive way to tell is to examine the SPI Library source code specific to the platform you're using.