Superhero Origins Question?

In the Silver Age comics continuity, they are both Superman’s cousin, Kara Zor-El. Supergirl is from the main DC Comics universe, while Power Girl is from the Earth-2 universe, where most superheroes debuted in the late 1930s & 1940s.

Supergirl was born many years after Krypton exploded on Argo City, which survived the planet’s destruction. When Kryptonite meteorites penetrated the city’s shielding, her parents sent her to Earth while she was in her teens.

Power Girl and her universe’s Superman were both born on Krypton. Their fathers both sent them as infants to Earth before the planet’s destruction. While Superman’s rocket arrived in the 1910s (so that he’d be an adult by the time of World War II), Power Girl’s rocket took many decades longer to reach Earth. Her ship kept her in stasis until it landed, so biologically she ended up decades younger than Superman on Earth.

they're alternate-universe versions of each other -- both are "Kara, Superman's cousin, from the exploded planet Krypton."

one didn't "change" into the other, they both exist at the same time.