As I see it, the confusion about kissing and hugging got started in the 17th century. The exquisite preciosity (and hypocrisy) of the Versailles courtisans - who called teeth "the furnishings of the mouth", for example - made it popular among them to describe having sex with someone as "kissing" them. It was less crude, but more ambiguous too, and it soon lost its euphemistic sense and became a word just as rude as f---. The result is that, until today, if you say that a couple is baise-ing, it means they are fucking, et point finale!
This expropriation, however, created a need for a substitute to describe the simple act of kissing someone, now that “baiser” had been irretrievably expropriated for another purpose. The solution created even more confusion - the verb "embrasser", to embrace, began to be used (or misused) instead.
The result of all this is that in current French one has to find all sorts of round-about ways of describing these simple acts. For example, to say "I want to kiss you", you can choose between "Je veux t'embrasser" or – curiously - "Je veux te donner un baiser", since the noun did not meet the same fate as the verb.
“I want to hug you” is even worse, since this gesture is not very French and, what with “embrasser” now meaning “to kiss”, has to be described in detail: "Je veux t'entourer des bras", "Je veux t'enlacer", or still "Je veux te serrer dans mes bras". Curiously again, the noun retains its original meaning – the seldom used “une embrassade” still means “an embrace”.
It's a lot simpler in English - and in Spanish with "besar", "abrazar" and "abrazo" - but that is the state to which the French mania for "la délicatesse et la discrétion" has led them and their beautiful tongue. It's one of the reasons that immigrants find it so difficult to learn French, and even leads native-born youngsters to butcher their own language and stuff it with English words. The alarming result is not just the much-decried "franglais" but a kind of pidgin which is inexorably forcing out the 17th century form of the language which we, who have laboriously learned it, still speak.
The proof that this last statement is true, whereas current English has immeasurably evolved over the last few centuries, is that the plays of Racine and Corneille are still clearly understandable to us, while those of Shakespeare are a minefield of misunderstandings that cannot be read without footnotes.