The bird in Breath of the Wild is NOT a Rito, but a Loftwing!
Take a good look at the following screens from BotW, WW, and SS.
As you can see, the bird in BotW has talons and not feet (as most birds do), a notable tail, and no visible ears, as well as a broad wing.
The Rito in Wind Waker very clearly do not have talons, and have something more closely resembling feet. They have ears that closely resemble the pointy ears of the hylians. They also don’t have any tail that we can see. Also instead of a normal beak, they have a beak-like nose and a separate mouth. The wings also appear more narrow, however this may just be due to the angle.
Links loftwing in Skyward Sword more closely resembles a traditional bird. Including talons as feet, a long beak that is both nose AND mouth, a notable tail, and finally, no pointy ears.
And if that’s not quite enough to convince you, compare to this concept art from Skyward Sword: