So, What's the Difference Between Batgirl and Batwoman?

Probably not! The CW has had eight DC Comics-based series: "Arrow," "The Flash," "Supergirl," "Legends of Tomorrow," "Black Lightning," "Batwoman," "Superman & Lois," and the brand new show "Naomi". So far, those series have all been contained into one universe together, known as the Arrowverse, since "Arrow" was the first show from the network. None of these characters or plotlines have crossed over into the DCEU, and there don't seem to be any plans to do so. Of course, as Keaton's entry into the DCEU shows, anything could happen in the future. The heads at DC might also decide to bring their own version of Batwoman into the DCEU and cast a completely new person in the role.