I bet it irked at least one or two 2nd Edition writers with a hard-on for the classics that the editors apparently allowed their feudal subjects to write up two or three wildly different kits with the exact same name, but a monster entry seemed to require a unique one, or at least appending a ", [NAME OF CAMPAIGN SETTING]" to the end of an existing one, which meant that once someone decided that such-and-such a name from Ovid "really" described an intelligent gastropod that used crystal technology to hop between planes, that was that. They burned through the list of mythical monsters pretty quick, too, between supplemental rule books and Dragon articles.
We're on firm ground here, again. The Yeti is a humanoid or possibly simian creature rumoured by local folklore to live in the Himalayas. The name "Yeti" is Napalese and means "snow man" in that language, but it seems to be descended from the Tibetan word "Yache" - which means "rock bear" or "cave bear" - so there is a good chance that the idea of them being near-human is due to a transliteration/translation error. According to Wikipedia, they have quite a few alternate names in the region, such as "man bear", "wild man", "cattle (stealing) bear" and "jungle man".
Given all the other cases we've had so far of real creatures being exaggerated into monsters, I'm pretty sure that the yeti is basically just the Himalayan brown bear, (which, like many bears, would sometimes have been seen on two legs). In fact, the bits of "yeti" fur that have been analysed have been shown to be Himalayan brown bear fur.
D&D's treatment of them has them as fierce and carnivorous, with white fur that lets them be camouflaged in the snow; although the ones from stories and supposed real-world sightings tend to be shy and have darker hair, just like the abovementioned bear.
Since you brought up both yetis and Asian bears, I am going to mention that a Podcast called Astonishing Legends did a yeti series. There's a famous photograph of a yeti footprint called the Shipton print. I think in the last episode of the three part series, they brought in a naturalist, who studied the wildlife in the Himalayas, and this guy said it looks like the Shipton print is the paw print of a particular bear in the Himalayas.
I did a search and nothing came up on this - does anyone know the origin of the genasi, particularly the name? I happened across this, and found it interesting that 'genasi' and 'sagani' are near-anagrams. On the other hand, the weakest type of genies that sha'ir use as familiars in D&D are called 'gens', so that might be the root word of the genasi race. (Al-Qadim and the sha'ir came out in '92, the Planeswalker's Handbook and the genasi in '96, so either seems plausible to me).