Damsel in distress is where the woman needs saving.

Fridging is where the woman has faced near or fully irreparable harm or death and the hero feels a need to avenge her as a result.

Because in the Green Lantern comic it came from, the hero's girlfriend got dismembered and stuffed in his fridge. Killing off female characters for the sake of easy drama is especially prevalent in superhero comics, extending way before this specific issue (see Gwen Stacy to start). But this incident is what prompted fantastic writer Gail Simone to coin the phenomenon's comic-related incarnation.

I think "fridging" implies more bodily harm (or threat thereof) than the traditional "damsel in distress" which is often a kidnapping or often a form of arranged marriage, though bodily harm is part of both. Either way, tropes change and can get new names over time, so I guess this might be a more modern term for an old trope with some new stuff added?

It was called fridging after one character literally had his girlfriend murdered and stuffed in a fridge. There was a lovingly rendered discovery scene.

Women dying for male character impetus is very different from "damsel in distress" Btw