More or less. Lot of semantics there, with blurred categories. Both garden tractors and lawn tractors are also referred to as riding lawnmowers. Garden tractors tend to be more powerful and may have other accessories like a plow or snowblower.
When I say lawnmower I envision my lawnmower, a 150cc push model. I never measured but the wheels are around 6" and made of plastic.
You are in sad shape. If you were in Canada they might suggest euthanasia.
Wheel sizes come and go. My father once bought a car because it had 15" wheels. The other US manufacturers had went to 14" and he didn't believe in 14" wheels. Or radios, automatic transmissions, and a host of other new-fangled stuff.
The first Toyota I bought had 14" wheels which is why I'm still running
14" winter tires. 15" wheels were optional. This one came with 15" but I believe 16" was an option. And it goes on from there. I think 20" wheels with tires that resemble rubber bands are the biggest but I'm probably wrong.The rolling diameter of the whole assembly depends on the tire which are all over the place. There's a lot of gaming the system. The Toyotas came with low rolling resistance tires that had a tread life of around 20k miles, ridiculous on a light car. However they improved the fuel economy which helped to raise Toyota's fleet average.
Look at something like the Toyota GR86. Thee base model comes with
215/45R17 and the premium with 215/40R18. I have a suspicion the 45% aspect ration on a 17" wheel winds up the same diameter as the 40 on an 18" wheel. Whether the average racer boy would benefit by the possibly stiffer sidewall is questionable but big wheels a kewl.