I always though that there was only one Supergirl. But there are many Batwomen/girls in the DC universe. ( To my knowledge )
Yes. Kara Kent/Kara Zor-El is and always will be Supergirl. In Apocolypse, though, they mentioned right off the bat that she was Superman's cousin, but then went into this between batman and superman that kinda made you doubt that she was actually who she said she was, but then, of course, quickly disproved any doubts making you go, "well, the why question it in the first place." It was, however, nice to see Kripto make a brief appearance.
As to batwoman, batgirl: Batgirl has pretty much always been the commissioner's daughter. In the Arkum Asylum game they mention Joker shot her through the spine, restricting her to a wheel chair and she ended up taking the name of "The Oracle".
Batwoman was created in the 50's to be Batman's love interest to dispel homosexual rumour surrounding batman and robin. The original character was named Kathy Kane. Ironically, Batwoman was recently resurrected as a Kate Kane and a lesbian.
The movie was done in the style of the old animated series from the 90s and, like I said, Kate Kane made no appearance, whatsoever. In fact, the costume made her look more like catwoman than anything else. It was stupid.
Mystery of the Batwoman gets a 4/10 - a pathetic attempt to reuse a character and I'm impressed that DC even let this movie be made.
Batman/Superman: Apocolypse gets a 7/10 - title doesn't really go with the story and there was a LOT of disjointedness to the story, but scantily clad women kicking ass, and the fact that they all but directly said that Wonder Woman essentially ran a fighting camp for lesbian superheros....yeah. But, the creepy incestuous relationship between Superman and Supergirl was kinda wrong...but in the end, Supergirl chose to be around a bunch of scantily clad women than Superman and Batman.