Obviously, the most glaring difference is that Chilling Adventures of Sabrina's Grýla is a witch. In this iteration, she has an origin story. During a terrible famine, she makes a pact with another witch in her coven: they would eat their own children to stay alive. After eating Grýla's only child, the other witch backed out of the pact, leaving Grýla devastated. According to Zelda Spellman, she's been wandering around, heartbroken, for 1,000 years.
So, in this version, Grýla is not an ogress or a demon or a horned creature, merely a woman gone mad. The Yule Lads still come into play; they get in when Miss Wardwell extinguishes the Yule Log's flame. They do have similar modes of troublemaking as well: door slamming, knife stealing, and so on and so forth.
The other major difference is that this Grýla no longer eats the flesh of children. Based on the way she speaks to little baby Letitia, it seems she adds children to her flock to fill the hole in her heart and to protect them. But hey, at least she's keeping some of the dark roots that stem from her origin.