"Not quite. 7.62 NATO Brass is thicker, so it therefor has less case capacity and will have slightly higher pressures for the same powder & bullet."
This is a difference in the construction of the case and not a difference in cartridge external dimensions or firearm chamber. It also isn't necessairly correct that 7.62 NATO cartridges are loaded to "lower pressures." It is true, however, that if one doesn't want to damage a a semiauto one must stay away from the slower powders and perhaps from the heavier bullets. This is not because of high pressures per se but because of a more prolonged peak pressure that can damage the operating rod.
Also, for those who would like to quote the Hornady reloading manual; the latest (7th edition) version does not list loads for 7.62 NATO. Is does, however, list loads for "308 Winchester Service Rifle" which were worked up in an M1A.
You might also be interested to know, that varying case volumes are not just unique to commercial vs military brass. There can also be volume differences between various brands of commercial brass; that doesn't make them a different cartridge.