Felicia isn't Selina Kyle; but in Felicia's fantasy version of her life she is. That is, Felicia is a slightly more grounded and rounded version of the more fantastic character she fantasises about being.
The difference between Batman/ Catwoman and Spider-man/ Black Cat is that Bruce/Selina works on a sexual tension and romantic level but are kept apart by Batman/Catwoman; but Peter/Felicia doesn't work even if they're sometimes thrown together by Spider-man/ Black Cat.