Technically, "wheel" refers to the part that has the spokes (or a solid disk) and the hub. Originally, the rim was a separate piece bolted to the wheel on which the tire was mounted. It still is on some large truck wheel/rim/tire assemblies. This is why wheels have "rim width" and "rim diameter". It's more correct to say "tire/wheel assembly" when referring to the assembly. In automotive terminology "wheel" is the metal part, and "tire" is the inflatable part.