Tires: tire size, sized tires, size tires

Question
So, what is the difference in running 45psi vs. 35 psi? I know what it stands for and all but why the different size tires if they are actually the same diameter? I looked into a blazer club as well and some are running 31's. Im just confused on the same-diameter different-sized tires. Thanks for the quick response.
Jim
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Followup To

Question -
I am looking for new tires for my 02 Blazer LS 4X4 2dr. The stock tire is 235/75/R15 and I want to upgrade without losing much suspension travel as well as having rubbing. I am going for an A/T tire. So far, I have found that a 31X10.5 is offered to replace the stock size but I think that would be too much. Do you think a 30X9.5 would be feesable for what I'm looking for without having problems?

Answer -
Jim,

The 31X10.50R15LT would be a better choice.  Using a 30X9.50R15LT requires you to use 45 psi, compared to the 35 psi for the 31X10.50R15LT.  And it has the same diameter!

Answer
Jim,

Opps!

That's what I get for trying to do this from memory.

The 31X10.50R15LT is slightly larger in diameter, but the 30X9.50R15LT is a bit smaller in diameter compared to the P235/75R15.

When it comes to load carrying capacity - air chamber volume and air pressure are some of the determining factors.  So the 30X95.50R15LT, which is smaller in diameter (a major factor in air chamber volume) and slightly wider (a minor factor in volume) result in the need for more pressure to get the same load carrying capacity, hence the need for the increased air pressure.