Macy is the unknown sister and is the oldest of the sisters. In the original, Prue was the oldest of the sisters and possessed Telekinesis. Paige was the unknown younger half-sister, who was half-Whitelighter and possessed a variation of telekinesis.
Macy is a scientist, while Prue was an antique specialist before becoming a photographer. Paige was a social worker and later the Headmistress of Magic School before eventually becoming a fulltime Whitelighter.
Paige was half-Whitelighter by blood, while Macy is a witch with demonic trait due to having been resurrected with demon blood.
The Source was the main antagonist for the first four seasons of the original series. He was the reason that the demonic assassin Shax was sent to kill the Charmed Ones, but he only managed to kill Prue. Piper and Phoebe discovered Paige when Shax also attacked her.
In the original, the Charmed Ones gain their powers through the reading of the Dominus Tritus spell. In the remake, the sisters' powers are unbound by their mother, Marisol Vera. The Vera/Vaughn Sisters each have a different father; while in the original, the original trio all shared the same father.
In the original, Whitelighters were not meant to reveal themselves to their charges, unless it was necessary. In the remake, it appears Whitelighters are allowed to reveal themselves to their charges when they meet.
In the original, Whitelighters teleported by orbs. In the remake, they have a different teleportation power.
Whitelighters in the original series did not have telekinesis while the Whitelighters in the remake do, or at least Harry does.
In the original series, the Halliwells weren't given a choice of whether they become witches. The remake gives the assumption the Vera sisters do have a choice and have 48 hours to choose whether they take up their powers.
There is an Easter Egg in the Vera Book of Shadows that stems back to Melinda Warren, the founder of the Warren/Halliwell witch bloodline from the original series. Currently, it is unknown as to whether Melinda in this new series is an ancestor to the Vera family.
Jenna's name might be derived from the short-lived character of Jenny Gordon. Jenny was the niece of Piper's third love interest in the original series, Dan Gordon. Jenny was written out of the original show because of negative feedback from fans who deemed the character unnecessary and annoying.
Despite obvious similarities shared with Natalie an Whitelighter from the original Charmed. Tessa got her name from an one shot character who was a college classmate of Phoebe's who ended up saving her.
Abigael tried to kill Macy at the end of Careful What You Witch For and in Deconstructing Harry, Mel called her "Abby". Ironically, there was a psychotic mortal in the original show named Abbey, who tried to kill Prue to replace her, because she was jealous of her life.
Mel and Maggie went back in time after casting a spell to find out what type of evil spirit they are dealing with by revisiting the spirit's past. In the original show, time travel was a recurring theme.
Macy, Mel, and Maggie lost their individual powers after going through a portal. In the original show, the sisters frequently lost their powers but nearly always get them back at the end of the episode.
In the original show, whenever a regular cast member was absent from an episode, their name and image in the opening sequence would be removed. In the reboot, whenever such absences occurred, the actors' names would be removed from the starring chart.