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The measurements listed in the tire specifications are typically done with a tire mounted on the Measuring Rim and inflated to maximum pressure. The dimensional notations (i.e. 35x12.50R17LT) are defined by an industry standard organization called the Tire and Rim Association (TRA). There are counterpart organizations in other countries - Europe has the European Tyre and Rim Technical Organization (ETRTO) and there are others. These organizations publish annual yearbooks that specify details about the tire size. Their purpose is to allow the OE manufacturer to design the appropriate size wheel well and to provide the end user (that's us) a reasonable expectation that a tire of a given dimension will be similarly sized regardless of tire manufacturer.
There is actually a design window specified by these industry standard organizations (TRA, ETRTO, etc). It is a plot where the horizontal axis is the section width (SW) while the vertical axis is the overall diameter (OD). I tried to find an example but couldn't turn one up in the limited searching I did online. What it means when I say 'window' - the TRA specifies a minimum and maximum value for both SW and OD for a given dimension. As long as the tire manufacturer puts the tire in the window they are abiding by the standard. I'll try to find an example of this later.
The OD measurement is taken in the center of the tread - it's actually a circumference that is being measured, then converted to the diameter. If you mount your tire on your vehicle and measure the height, you'll be sorely disappointed when you see that your tire doesn't measure up to even the spec listed on the spec sheet. Of course that's because under load the tire will deflect. Although not typically published for passenger car tires, in the Truck tire world we often publish the static loaded radius (SLR) - that's the distance from the ground to the center of the tire when the tire is mounted, inflated to max pressure, and loaded to max load. Note that 2 x the SLR is NOT equal to the tire height on your vehicle.
If you mount your tire on a rim that is not the same as the measuring rim, you can also expect to see some variation in OD and SW. Narrower rim will result in a narrower and taller tire while a wider rim will result in a wider and shorter tire.
Hope that sheds some light on the measurement situation. I'll try to find an example of the design window.