I don't have any formal pony club levels -hides-
I am, however, in the second-from-highest group for the group lessons, and my coach keeps telling me to forget about riding 'pretty' (as a reference point, I took lessons with the same coach about 2 1/2 years ago and he was ALWAYS telling me off about something to do with my position).
I think the moment you really become an 'intermediate' level rider is when you start to be able to really engage your core, and start to feel how off-balance you REALLY are. You feel like you're going backwards for a while, and then the improvement takes the bit in its mouth and gallops away with you! Your confidence soars and your results (if you show) improve dramatically. Your horse is responding better, that one little niggly thing that's been driving you nuts that you always thought was your horse vanishes when your coach tells you "just put a little bit more weight in your inside stirrup" and you do as s/he says. You learn the feel to know the difference between a lazy trot and a really good working trot, and the difference between a good extended/lengthen trot and a rushy flat 'fast' trot - the difference between 'fast' and 'forward' comes to you as well. You might know the difference between the LOOK, but until you know the difference between the FEELING, you'll never get the right results from your horse.
Intermediate is the place between your coach telling you 'better' and your coach telling you 'NOW you're ready to help train that OTTB, with my guidance'. Intermediate is the place where your coach stops saying 'better' and starts saying 'GOOD'. That's if you have MY coach, who is amazing, and who is very tough on his students. If you have the big softie next door, "amazing" might mean "wow, you can canter without falling off, well done!", and if you have the mean lady with the stick who will literally smack you if you so much as waver half a step of the centre line, "ok" might mean "you amazing rider, that was PERFECT, can't fault your piaffe/canter pirouette/insert other extremely advanced dressage movement, and I feel threatened now so I won't tell you how great you really are"