Definition on the webster says that prostitution is :  the act or practice of engaging in promiscuous sexual relations especially for money

The word “especially” is vague so we can remove that from definition and comeback to that latter.

Sugar babies are not promiscuous. Also sluts are not usually considered prostitute. So why are sugar babies considered prostitution and sluts are not?

Wikipedia definition says: Prostitution is the act or practice of providing sexual services to another person in return for payment.

Well, marriage does pay. Just ask ex wife of Beatty Chadwick http://freebeattychadwick.blogspot.com/. So why marriage is not prostitution while being a sugar baby is?