A B.S. or B.A. is considered an undergraduate degree, a college degree received after high school/GED. A M.S. , M.A. of MBA is considered a graduate degree which can only be obtained after you have received an undergraduate degree of some type (although some schools offer a combined bachelors to MBA program). FYI, this is not a complete list of undergraduate or graduate degrees.
Also, an associates degree is another type of degree received after high school/GED that usually requires 2 years of study. Some people obtain an associates degree say from a junior or community college and then transfer that credit to a university to count toward obtaining a bachelors degree.
I received a B.S. engineering and then attended graduate business school. I received an M.S. instead of an MBA in graduate business school because of my electives. So I took several accounting, economics, finance and marketing classes but my electives were solid programming classes like C and Visual Basic. So the difference between a B.A and B.S or an M.S. or MBA in business school would possibly be the electives or other core curriculum that are more science based.
Hope this helps.