There have been several incarnations of Supergirl (her Kryptonian name is Kara Zor-El), and they are: (from left to right): The Original Kara Zor-El, Matrix, Kara in the '70s, Modern Kara, Linda Danvers, Power Girl, and Kara from Crisis on Infinite Earths.
The Art in this piece is by Ed Benes.
Powergirl is an alternative universe (Earth-2) version of Kara Zor-El, who usually goes by the name of Karen Starr.
Matrix was an artificial life form made of a "protoplasmic matrix" that took the form of Supergirl.
Roger Lee is a life-long comic book and sci-fi aficionado. As such, he fell into the habit of writing about the superheroes and sci-fi scenarios that he reads in the comics and books and sees on screen. Since writings on superheroes need to be shared, he has written for web audiences for years. His writings have appeared on www.comicshistoryguy.com, www.comicbookmovie.com, www.bamsmackpow.com, and now in superheroreviews.com.