Is it normal that I'm the teenager my mother used to be?

I’ve been thinking about it, but I’m not sure why it’s happening. I’ve changed a lot since last summer, and I think I’m too much like my mother. When she was a teenager, she would listen to The Doors, read a lot, draw, write poems, etc. Now that I’m 14, I’m exactly like she was. I don’t think it’s bad, but I don’t want to be my mother. It’s great when she and I talk about poetry, or Jim Morrison, etc, but I don’t wanna be the same person she is. I’m changing all the time, so I don’t know how I’m going to be in the future. I have my dreams and my plans, and I’m much different than her sometimes, but I’m worried about how similar we are. Is this normal?