Native code:- This term is sometimes used in places where machine code (see above) is meant. However, it is also sometimes used to mean unmanaged code. Unmanaged code is the kind of code that requires you to manually allocate and de-allocate memory, sometimes causing memory leaks (when you forget to de-allocate) and sometimes segmentation faults (when you de-allocate too soon).
Machine code:- This is the most well-defined one. It is code that uses the byte-code instructions which your processor (the physical piece of metal that does the actual work) understands and executes directly. All other code must be translated or transformed into machine code before your machine can execute it.
Assembly code:- This term generally refers to the kind of source code people write when they really want to write byte-code. An assembler is a program that turns this source code into real byte-code. It is not a compiler because the transformation is 1-to-1.