Is Gerda in the show meant to be the same Gerda from the original Snow Queen story?

I stupidly just now realized that they share the same name. Are they supposed to be the same character or is there another Gerda? Is it that since Gerda's daughter, Anna is based off of the original Gerda and her other daughter, Elsa is based off of the original Snow Queen that they made Gerda sisters with the original evil Snow Queen? I'm so confused and embarassed since I just now got it lol