My understanding is that a digital piano means it is intended to mimic a real piano, which it does so in two important ways. One is with weighted keys, which is meant to feel like the resistance real piano keys have. The other is with velocity sensitivity (not sure if that is the technically correct term). It basically means that the harder you press, the louder it plays (like a real piano).
I think the term keyboard is used for instruments which don't do these two things. The other issue with keyboards is that sometimes they will only play a limited number of tones at a time. I think this is referred to as polyphony. Mine plays 64 notes at once, for example. I have a Yamaha P-85. It is their entry level digital piano. I've been very happy with it. Also, make sure you get one that you can attach a full set of pedals to. That's an important element of piano playing that you should learn from the start.