Obviously, "the price of a car" can also mean the price of a car in general, so I am wondering if "car prices" and "the price of a car" are basically synonymous.
There is some overlap, but car prices carries more of a connotation of representing the full range of prices on the market. In some contexts, they are pretty much equivalent:
The effect of the exchange rate on the price of a car/car prices
But in others, they are not:
He has an amazing knowledge of car prices.
The price of a car is not car prices.
Car prices are the prices for cars in a market. "Cars prices" is plural and general. Car prices=the prices of cars, with an s.
The price of the car in the parking lot is $10,000. The price of a car in my area is not cheap.
A plural noun and a singular noun are not the same thing.