CONFUSED ON WHATS "NORMAL" IN A RELATIONSHIP

I was in a relationship with someone for a few years who was controlling-- calling me 10 times a day/texting me constantly/always wanting to know what i was doing.. he said it was being he loved talking to me a million times a day because i was always on his mind.. This was my first & only real relationship. We are now broken up and I am seeing someone new. However, since this was my first relationship, I've grown to think that this is normal.
I talk to this new person in the morning and sometimes at night.. Since I am so used to talking to my old boyfriend so many times a day, I'm beginning to think that the new guy doesn't care about me.. When we are together he's the sweetest, most caring person, but when were apart, it seems we don't really talk much. I don't know if he is just terrible with the phone or if it's me.. I'm confused on whats normal in a relationship!