To my knowledge, handgun round case gauges are chamber gauges and are supposed to be cut to minimum chamber dimensions. They are meant for checking to see if a round will chamber without using the actual firearm.
So, checking for chambering a 38 Special round in a 357 Magnum gauge should work fine. Although, if you are using the 38 Specials rounds in a 38 Special firearm, i could see a slim potential of the round fitting the 357 magnum case gauge and not the firearm's chamber. Depending on how the case gauges are made, case length would be the issue. But, that is only a guess on my part.
For handguns, there is no better chamber gauge than the chamber of the firearm that the rounds will be used in. For safety, remove the barrel (semi-auto pistol) or cylinder (revolver) before using it as a gauge.
As an aside, case gauges for bottle neck cases are not chamber gauges for the most part. Most commercial gauges measure overall case length and shoulder position (headspace) only.
If you are looking for a chamber gauge for rifle cases, read the fine print on what the gauge does before you buy.