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.