tl;dr: The recommended pressure is almost always a good general recommendation. You can make adjustments to suit your specific needs.
The original recommended pressure (31 psi) applies only to the same
tire, or it's a characteristic of the vehicle (and should be used no
matter what tire I use) ?
As a first step, I'm going to point you at Tire Rack's excellent discussions on tire pressures and a whole host of other technical topics.
31 psi is a reasonable starting pressure on your vehicle, regardless of the specific tire that you put on it.
Let's quickly consider some of the factors that the air in the tires affects:
- It acts as a spring. We don't drive on solid rubber tires for a reason: these are much more comfortable.
- It defines the tire's shape. More air => taller tire with a smaller contact patch. Less air => shorter tire with a larger contact patch.
- It defines the tire's stiffness, especially in terms of the sidewalls. An underinflated tire is going to roll over its sidewall in a hard turn, wearing out the side and edge. A well-inflated tire will hold its shape, keeping a more defined contact patch on the road.
Now let's talk about examples of where we'd potentially like to adjust our tire pressures. Note: all of the factors below assume that you're tuning by relatively modest amounts (e.g., plus or minus 10%). So when I say "more air," I don't mean 100psi, and "less air" is not the same as saying "zero air."
- A front engine car is heavier in the front than it is in the rear. It is common to see a higher tire pressure in the front partially as a consequence of this increased load.
- Street cars are generally set up with a bias towards understeer. Lower tire pressures in the rear will increase grip on the back end, reducing the chance that it will swing around on a casual driver.
- A tire is an undamped spring (i.e., no shock absorber). A high tire pressure will transmit more of the bumps and jolts of a lower quality road directly to the driver. This factor increases in importance in proportion to the annoyance of the spouse in the passenger seat.
- A tire with less air will generally have more grip in all respects. This means that it will feel less responsive to sudden steering adjustments. A small drop (e.g., 2 psi) is common to increase winter traction where real snow accumulation is common and persistant (i.e., not where I live).
A severe drop in pressure will cause the sidewalls to bulge out significantly and dramatically increasing the footprint of the tire. This can be used to get out of a deep hole in the snow. You can see a practical example of this technique in the Top Gear Polar Special.
- A tire with more air will have a smaller contact patch and stiffer sidewalls, generally leading to increased fuel economy.
In short, tuning the tire pressures is the absolute cheapest way to adjust your suspension performance.
Nitpick: yes, I know that it's not the air alone that's acting as a spring. It's the combination of the air, rubber, belts and the deformation that happens under an impact. For an introductory discussion, though, we can say "air = spring."