The words are not synonyms, though some may incorrectly interchange their them in the US. Tires are mounted on wheels. Some may consider a tire to be part of a wheel, I'm not sure which is correct. But on a bicycle, spokes are part of the wheel, not part of the tire. On a car the rims are a part of the wheel, not part of the tire.
I'm not arguing that point. But if Duo included the word for tires then I would have just kicked myself and gone on. In effect, the wheel is the whole unit which rotates from the axle. The tires, the rims, the spokes, all of them are a part of the wheel.
And, as I look back at this, I can see that asking for Duo to include pneŭmatiko, rando, and spokoj is just getting more technical than some may be ready for.
I see. I suppose the primary confusion is the inaccurate (American) phrasing of "changing a tire (on a car)," and "spare tire". The spare tire include a spare wheel. And changing the tire requires changing the wheel (because of how car tires work).
Perhaps the confusion also comes from our country's worship of cars. On a bicycle changing a tire (tube) and changing a wheel would mean different actions done for different reasons. The distinction exists for bicycles because it is possible for people to mount tires on wheels, and then inflate those tires, themselves.
The phrase given by Duolingo does not specify that a car needs its wheels changed. But I suspect that many people (myself included) made that assumption.
When I lived in Russia, I did change tires on my car's wheels twice a year, though. From winter tires to summer and backwards. This involves going to the tire service, where they do it in 15 minutes. So it is also also common to change tires without changing wheels on some regions.
I agree, tires should be accepted. Most people don't own rail cars that travel between Russia and China. It might be an American and probably Canadian idiom, but that is a very large and world influencing segment of the English speaking population and therefore it should be accounted for and accepted. Like someone said above, wheels could be in the Duolingo translation, and we would learn from that.