FWIW, all the P- series tires (P205/75/15, P235/75/15, etc) are technically classed as "car" tires. The LT series tires (LT235/75/15) are classed as "light truck."
Since Rangers typically come with P series tires on them, I'd say they come with a car tire.
Going to a less-aggressive tire will quiet out the noise from the tread. A larger tire like a P235/75/15 inflated to 30-35 psi will give a softer ride as the larger sidewalls allow for flexing to help absorb bumps. Going to a smaller, skinnier tire like a P205 or P215 will help with fuel economy. But I wouldn't be expecting anything significant for a change in anything. At the end of the day, it's still going to ride, sound, and suck down gas like a truck.
I ran P235/75/15 tires in an aggressive AT pattern on my Ranger. Not overly quiet, but I needed the traction and was happy with how it performed. My F-150 gets nothing but LT tires (currently running 31x10.50x15 tires) of an aggressive AT pattern which are pretty noisy. A P-series tire would probably be a good bit quieter, but I need the traction and I need the load rating since I use it like a 1-ton a lot of the time. So it's all in what you're looking for.