The reason why I ask is because tires can gain pressure (psi) when being driven (heat gained from friction which increases internal tire pressure) so I'm not sure what that number exactly entails. Does the manufacturers suggested inflation pressure mean the pressure in the tire should match that value at all times? Tires gain psi when being driven so how is it possible to always be at that exact psi value unless I'm constantly changing the psi in the tires. I'm guessing the number set by the manufacturer is in reference of the minimum value that a cold tire air pressure should be set to. This would mean that slight over inflation is better than under inflation from a practical standpoint. Am I wrong?
It is actually far more complicated than that.
The manufacturer suggested tire pressure is for the tires, cold, before driving. The problem with this is the suggested value is for the specific tires that the car came with. It is possible to replace the tires with ones that would be over inflated or under inflated by the suggested value.
Cars normally come with 44psi max tires. There are 35psi max tires. Inflating them to the suggested sticker would be over inflating them.
Many trucks come with 44psi max tires. There are 55psi max tires (load range E). Inflating them to the suggested sticker would be under inflating them.
Follow the recommendation for the tire not the car.
Then the manufacturer sets the cold-inflation pressure they're aiming for a desired pressure at running temperature. They adjust that down to a cold-inflation pressure by assuming a given amount of temperature increase from cold.
Manufacturers tend to set the recommended pressure toward the low end of the desirable range to give a softer ride. (At least, for typical passenger cars.) So, yes, slight over inflation is definitely more desirable than slight under inflation.