I generally think of medium as being of some sort of the middle of a **static** range, (statistically it is defined as the value halfway between the mininum and maximum values), *such as being of* ***medium*** *height*, while intermediate is about the middle of a **process** such as *the* ***intermediate*** *level music examinations are what you would have to pass through to get from beginner level to advanced level*.

The other difference is that a specific sample might not contain any of the medium value but a range of states must pass through the intermediate value as they progress.