I actually have a digital. In fact I have something somewhat better than a digital: a hybrid (Yamaha N1). It has the action of a grand but I can still use it in an apartment.

I also thought this would be good enough, but after taking lessons it's obvious that it's really not. Even though the action is supposed to be that of a grand piano, the reality is that when I actually try to play on a grand I can't play it. My teacher has also said that I really need to get an acoustic piano.

I'm not entirely sure what it is, but I think the main difference is that even if the action feels like that of a real piano, it doesn't react quite the same. There are a lot more subtleties that you can get from a grand piano that's just not possible from a digital with the touch and especially with the pedal.

Note that this is for classical music, I don't know a thing about Jazz or pop music.

I really do appreciate your trying to help though!