ORIGINAL: simovitch
Generally speaking, regarding the actual plate used for testing, does the penetration (mm) listed mean that a plate of that thickness was used,...
No.
Say the Germans took a high performance 75mm gun (say the German Panther 75mm KwK 42 L/70), then they considered the penetration performances of comparable existing guns or identical gun designs (say a PaK barrel), most likely, and I guess they then computed (roughly) what penetration depth could be expected (probably taking into account the [muzzle] velocity), before commencing any live fire testing.
The test environment is quite important, means it really matters what material is put behind the test plate. If the material behind the plate is harder than the actual test plate, then it's more likely that a rather "thin" plate is being penetrated (well, physics :p). In other words, such a setup makes it somewhat easier for the round to penetrate, so the round will penetrate more armor as compared to a case where "softer" backing material is being used.
That's why today's penetration tests are standardized in a way that there's a certain backing material (forgot which one) projected to be used, in order to make results comparable. Did the Germans employ such standards? Or the US? You'll have to research that.
EDIT: If I am not mistaken, JENTZ points out that at least the Germans used 30° (from vertical?) as standard setup, plus they used the same types of what they called "homogeneous" armor plates, so that results could be compared.
Some sources indicate that these plates were of better quality, means like a type of reference plate. I am not sure whether that's true or not, as I think it was Jentz who pointed out that the steel grades (coming from the different foundries) for quality assurance and tests (yes even test shooting) were in fact samples, so it's hard for me to believe they conducted tests on "best" plates.
On the other hand, I have not read anything about German armor production/testing from other authors (if there are any who cover that topic).
http://www.panzerworld.net/75l70
http://www.panzerworld.net/armourpenetration
My personal guess is, that the US were less consistent there, means one or another field or lab test was commenced using vertical plates, it seems.
...or that the projectile in question embedded in some generic plate at that depth?
Well, for the Germans, see my ref. to the "homogeneous" plate above. Probably a plate of say 200mm or even more, to cover all possible results (say with Panther gun, KingTiger, or even prototypes like the PaK 80 L/54,8 [also dubbed PaK 44, K 44 or K 81] - this gun could penetrate 201mm of armor at 1000 meters [30 degrees]). The exact setup is unknown to me, you might find it in Jentz, and probably in his works or works from other authors for US procedures.
Example below: did the 75mm Gun penetrate a 60mm thick plate from 457m that was sloped 30 degrees from vertical, or did the testing entity (lets say USA in the 30's and 40's)use a standard block of armor (sloped 30d) and measure the depth of the resulting impact to be 60mm deep?
I've seen some shady references on the net that indeed suggested that with some tests the US were just interested to see if they could penetrate the frontal armor of a given enemy tank, so that they took plates (and an according thickness) that would indeed "just" simulate the front plate of let's say a Mark IV tank, or they even took an enemy tank (eg. field tests in France, 1944). Jentz and others may have shed some light on that speculation, I don't know whether the mentioned refs are just wild speculations or not, sorry.