"stare" is more physical, we use it to answer (and make) questions like:
How are you? (asking the physical state) - Come stai?
I'm fine - Sto bene
"Come sei", on the other hand would ask the essence of the person, the meaning is more like "describe yourself" than anything else.
"Stare" is time related, as you ask "come stai" you mean how are you now. in this moment, when you ask "come sei" you mean in general, not relate to time, "How are you build"
The difference becomes less significant when we talk about places. You can ask "Dove sei" or "dove stai" with very close meanings.