There have been many different versions of Supergirl over the years. Throw in Power Girl, who is a Supergirl variant, and there are even more. So, as a comic reader of many decades, I’d argue there is no “real” version of Supergirl. The new Supergirl movie, continuing James Gunn’s vision of the DC Universe, takes Kara Zor-El’s story forward, based largely on the “Supergirl: Woman of Tomorrow” arc from the comics.