What's the difference between a "stay-at-home-mom" and a "welfare mom?"?

today on the radio they had an author who was promoting being a “stay-at-home-mom.” i was wondering why we use this term for some women but not for women who are poor and on welfare. it seems the term is used exclusively for middle or upper class women.

It seems that in our society, we perceive mothers who receive public assistance and moms who have husbands who make enough to enable them to not have to work as something different. At least the perception of the wording “stay at home mom” and “welfare mom” impllies something different.