The difference is Kate was an established civilian (in superhero terms) living in Gotham. She knows who Batman is but it is her interaction with him that sets the thought in motion. She assumes the mantle of the Bat - since even though she doesn't know him personally, she makes his war against crime and his methods (like Batman's "no killing" rule) her own (as a US Army soldier she would have been prepared to kill, as a "Bat" she is not).

Diana got her powers from the Gods, is sent to by the Amazons to be their Ambassador/Avatar, she doesn't live in Metropolis, doesn't know Supes from Adam. She has her OWN mission and her own way of super-heroing things that doesn't need Superman at all.