In reply to:

Didn't "baiser" originally denote the act of kissing, though? i know that the contemporary French word for kissing is "embrasser"

As a noun it means A KISS. Usually people say Donner un baiser - give a kiss.

As a verb it means
a) the act of giving a kiss (dictionary definition only. NOT used by population at all)
b) the act of making love (originally classified as vulgar but now part of common speech and generally the only accepted definition).

Embrasser is definitely used to mean giving a kiss, it also means adopting something, someone or some idea wholeheartedly. I believe in France it also means a hug but is not used in this way at all in Québec.For some reason we do not have any word to specifically mean hug in French Québec.