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 important point is that a given case may have several ***intermediate*** levels or states but will only have one ***medium*** point.

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.

To use them in a physics sense I would say:

 - in a set of samples for stress testing a medium sheer point of 10 N was found **but**
 - in all samples 7 N was found to be an intermediate point between the elastic limit and the sheer point.

In your coupling context I would say that possibly single a system can be strongly coupled or weakly coupled and has one _or more_ **intermediate** levels of coupling but if each of a set of systems can only have one level of coupling then the middle level between the highest and lowest will be **medium** coupling.