I don't understand the difference between Supergirl and Powergirl. Are they the same person but one is older? Are they from different universes? Is one a clone of the other? Or are they two completely different people?
Power Girl is a Kryptonian from the Pre-Crisis DC Universe's parallel world of Earth-Two. Earth-Two was where some of the earliest and most popular heroes from the Golden Age of Comics (World War II to the late 50s/early 60's) were assigned.
- Power Girl would be the analog of the Earth-One Supergirl, in effect, she is a parallel universe version of the Supergirl from Earth-One. In the strictest sense of the word she IS Supergirl. But that would change in the almost thirty-five years since her creation.
Pre-Crisis Earth-Two was a parallel universe where characters from the Golden Age of Comics were assigned after DC decided to recreate the Golden Age heroes in a more scientific format.
Stemming from a seminal tale called The Flash of Two Worlds, we are introduced to the characters of early DC Comics before DC owned the properties. These stories included the Golden Age Flash, Green Lantern, Wonder Woman and Superman. All of these characters were assigned to Earth Two.
Before the Crisis on Infinite Earth, DC had multiple worlds where they assigned characters from different continuities purchased by DC. Earth Three was populated by evil versions of the Justice League, called the Crime Syndicate, for example. (They make their appearance in later properties by the name of the Justice Lords on the JLA/JLU Animated Series.)
DC had many worlds and there was little some difficulty keeping track of which continuities did what. On Earth Two, for example, Kal-L married Lois Lane, Batman married Selina Kyle, Robin grows up but does not become Nightwing. Since the Golden Age heroes appeared to be aging (still slower than reality but faster than they do in comics) DC rebooted the Silver Age of comics with newer, more powerful versions of their Golden Age counterparts.
- Power Girl was Supergirl in the Earth Two Universe. When the Crisis on Infinite Earths took place, (a marketing decision to bring the continuities of the DC Universe on to one prime Earth), Supergirl was killed during the Crisis. Another decision to recreate the Superman mythos with Kal-El, the Earth One Superman as the ONLY Kryptonian alive.
- Power Girl, now a refugee of a destroyed universe, found herself on the single Earth of the DC Universe with a completely rewritten origin as an Atlantean, her powers the result of their scientific exploration and sorcery. During the 90's, Power Girl's origin and costume changes were legion.
- With the newly recreated Multiverse of the DC Universe, Power Girl is once again a survivor of a Krypton from a parallel Universe. She resided on Earth Two but was flung from her world to Earth One - Prime Earth, and will be returning to her world in a new series.
In the DC New Universe:
On the parallel world known as Earth 2, Power Girl is Kara Zor-El, the cousin of Superman. Like him, she came to Earth from the dead planet Krypton. But though they were sent from that planet at the same time, she arrived decades after him. In that time, she'd aged only months, and arrived in perfect health. At this time, Superman kept his cousin Kara hidden, as his secret weapon in their war against Steppenwolf and Apokolips.
She met her best friend, Robin aka Helena Wayne, on the day that Helena's mother died. When Robin rushed into a burning building, furious with grief, Batman called to Superman for help. Superman sent Kara to rescue Robin from the building. (Worlds' Finest #0)
Batman eventually devised a virus to take down Apokolips' forces, but he, Wonder Woman, and Superman were killed in seeing it to fruition. Supergirl was unable to prevent her cousin's death, but after the plan succeeded, both she and Robin plunged into a portal in pursuit of a figure which they presumed was from Apokolips. Whoever it was, the person eluded them and they emerged on a parallel Earth with no way back. (Earth 2 #1)
REF: Cosmicteams.com Power Profiles: New Universe, JLA, Earth -2, Power Girl's history