Does a mother incur sin by using the word "I have gifted" instead of "I have vowed" when dedicating her children to Allah, and what is the difference between the two expressions, and how can she correct her mistake if she has committed a sin?

Children's vows are not valid. The vow made by Mary, peace be upon her, was permissible in their law, not in our law. Furthermore, children's dedication to God is not considered binding, because everyone in the heavens and the earth already belongs to God. You will be rewarded for your intention to raise your children in obedience to God. We advise you to fear God and strive to raise them well.