Nope, the CPU presents you an interface of the available instructions but those instructions are a complete fiction on modern processors and don't have to match at all what the underlying hardware does. The CPU guarantees that the observable effects of the instructions are consistent (i.e if the processor wants to do some fuckery it can't change the instruction semantics) but beyond that is free to run your code however it wants.
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.
