Mother

Both star Ashida Mana. About the lives of children from abusive/unstable homes

Both have ....

-same writer
-Kurashina Kana <3
-some suspense plots
-(very) depressing tone in the start of series, but gradually become more hopeful
-somewhat unique and beautiful ending

Mother is the original version of the story. Though Saving Grace makes some changes as an adaptation, the main theme is the same.

Both are about a little girl being abused by her mom and step-dad until someone steps in and takes her away in order to save her.

It does feel like a short version of the TV drama series.
-protecting a kid against an abusive family.

This is an adaptation of other one.