Wheel diameter (e.g., 16 inch) is certainly a factor, but so is the width (6 inch, 6.5 inch, 7 inch, etc.) because it determines the range of tire width that will be suitable without rolling over the sidewalls in turns, etc.

You will see the width stamped on the wheel, such as 6.5x16x25, which are the width and diameter in inches, and the offset in millimeters.

I have 6.5x16x25 optional Volvo wheels called "Hydras", and I have 205/55-16 tires on them; they're a bit tall (the speedometer is off), but they (being Michelin Pilot Exalto PE2 in W speed rating) are very sticky -- excellent cornering and braking on both wet and dry pavement; and suicidal on snow, so I also have snow tires (Nokian Hakka 2) for the winter season.