What Westerners call the Yeti is very likely a real animal, in fact people actually living in the Himalayas who have seen them describe two distinct animals.
The first is the Tibetan brown bear (Ursus arctos pruinosus), a subspecies of the brown bear. The brown bear is a single species that occurs widely throughout the Northern hemisphere and includes the American grizzly. The Tibetan brown bear stands up to around 7 feet tall on its hind legs and has a very distinct coloration with shaggy brownish orange fur. The areas of lighter coloration are probably responsible for the theory these bears may carry some polar bear genes. These bears generally live above the tree line in the Himalayas but are quite rare. The Asian black bear lives in the forests below the tree line. They are black with a distinctive white crescent on their upper chests and slightly smaller. Like other bears Tibetan brown bears are plantipeds, walking on the soles of their feet like humans with feet and tracks approximately the same size and shape as humans. They hunt mostly marmots but also occasionally kill sheep, goats, and yaks, and very rarely humans have been killed or seriously injured by them.
Tibetan brown bears are a known species that lives in the areas where Yetis are reported, and are identified by locals as one of the two types of Yeti. Also DNA tests on Yeti hair samples have confirmed they came from Tibetan brown bears.
Photographed Yeti tracks, including those crossing steep snowy slopes in a straight line with no offsets have been cited as evidence of a large bipedal animal, but think it through. First, bears, like many large predators, tend to place their hind feet where their forefeet have been. This is a natural adaptation that enables their hind feet to have the same advantageous footing they could visually ensure for their forefeet.
Also when an animal crosses a steep slope its tracks will normally tend to form a straight line rather than be offset up and down the slope. This is a much more efficient manner of walking that ensures the center of mass doesn't constantly shift up and down the slope. Thus on steep slopes it's clear that bears can produce the single straight line of tracks often mistakenly attributed to a large biped.
In addition tracks in snow often tend to become significantly larger than the feet that made them as they melt. This is likely why some Westerners have assumed Yeti's are much larger than they actually are and attributed them to the long extinct Gigantopithicus.
However eye witnesses and other reliable residents of the Himalayas do describe a second type of Yeti. This is an ape like creature covered with fur with a humanoid face that stands around 5 feet tall. The most likely candidate here is a subspecies of the Orang Pendek. The Orang Pendek is a fairly slightly built darkish gray great ape or possibly even a surviving hominin about the size of a human. Sitings have been widely reported from SE Asia especially in Sumatra and this animal almost certainly does exist though it's as yet unknown to science.
So a hairier Orang Pendek adapted to live in colder higher altitudes in the Himalayas would simply and precisely explain the sightings and descriptions of the 2nd type of Yeti. This Yeti type is, like the Pendek, very rare and elusive but almost certainly does exist.
Thus it appears what Westerners call the Yeti is actually two distinct quite rare animals and both actually exist.
As for the Sasquatch, it seems highly unlikely that a giant ape could remain undetected for years in the Western US and Canada given the amount of hunting and other human intrusion. So one has to assume the legend, which apparently does precede Europeans, is based on the grizzly bear.