I'm not sure I understand the distinction (quite possibly just 'cause it's early).
A fruitful way to look at monads is to say a value of type M (where M is an instance of Monad) is a program in a language. State is a language for describing stateful computation. Reader is a language for describing parameterized computation. ST is a language for describing controlled, local mutation. IO is a language for describing arbitrary side effects.
Most of these have pure interpreters, with the most generic typically called runM (so, runState, runReader, &c). The only place cheating comes in is unsafePerformIO - interpreting IO is the job of the runtime, which does it in a more controlled way relative to the rest of your program.
The type of the return value of an interpreter, of course, doesn't tell you what kind of program you ran - it just tells you the result.
A fruitful way to look at monads is to say a value of type M (where M is an instance of Monad) is a program in a language. State is a language for describing stateful computation. Reader is a language for describing parameterized computation. ST is a language for describing controlled, local mutation. IO is a language for describing arbitrary side effects.
Most of these have pure interpreters, with the most generic typically called runM (so, runState, runReader, &c). The only place cheating comes in is unsafePerformIO - interpreting IO is the job of the runtime, which does it in a more controlled way relative to the rest of your program.
The type of the return value of an interpreter, of course, doesn't tell you what kind of program you ran - it just tells you the result.