An egg donor is the woman who donates her oocytes for an embryo to be created from them. She replaces the intended mother's uterus in the case of heterosexual couples, and contributes the female cell to the fertilization process. This means she is the biological mother of the child, and therefore the one who passes her DNA to the baby.
A gestational carrier is the woman who carries the pregnancy to term and gives birth to the baby for the intended parents. She is not biologically linked to the resulting baby.