Simpler RISC designs, like simpler ARM cores, more or less directly execute instructions; same for old 8-bit cores you can still widely find in MCUs. Complex high-performance cores, with pipelining, instruction fusion, and OoO execution, turn instruction stream into a microcode lava.
So maybe the right thing to say is that assembly is a contract between you and the processor and the underlying implementation can map directly to hardware when appropriate but it doesn't have to. It is an abstraction over different underlying hardware implementations.
