Moms is a term that is the plural form of the word Mom which is essentially an alias for the term Mother. Most people consider the woman who birthed them as their Mother or Mom, and call them as such. Moms is usually a term used as the main category after a subcategory. For instance there are Soccer Moms, and Military Moms.
The word Moms is also slang for one’s mother in the English language. For example someone might say “I need to go see my Moms” instead of saying “I need to go see my Mother.” This derivative of the word mother is used in urban settings usually by those on the Northeast side of the United States.
The word Moms isn't as heavily used as the word Mothers, as the term Mother's is used heavily in conjunction with the day for Mothers around the world, Mother's Day.