Each OS has its own set of system call which is been used by library. These libraries at the end will be translated into machine language for the processor.
Each Processor Architecture has its own set of instruction know as Instruction Set Architecture(ISA). So when a program written in high-level-language (like C) is compiled, it should be converted into machine language from its ISA. This job is done by the compiler(gcc). A compiler will be specific to only one processor architecture. For example gcc is for x86 processor. So if you want a compiler for different processor in you x86 machine you should go for a cross-compiler of that processor.