The 'many loves' definition of polyamory acknowledges the ability of certain people to maintain an ongoing, romantic loving relationship with more than one person at the same time. It may be a situation in which there is a primary partner and one or more secondary partners, or there may be several partners of equal 'status'. It actually goes directly against the idea of there being "one true love", and recognises that a person may have many soulmates.
The various relationships may, or may not, involve sex, but will always involve love, and in this case the two words are definitely not synonymous. Polygyny is defined as having many concurrent sexual partners, without the intimation of there necessarily being romantic love involved in all cases.