I've run into this a few times, and the short answer is no, they're not standard, they vary by mfgr. That said, "incompatibility" in my experience means the pieces won't fit and will leak.we replaced our toilet top when the old one cracked, my wife purchased a new tank, but a different brand.
now the water lvl in the bowl is way down and doesnt seem to have enough pressure to flush.
is it possible to mix the tank and bowl from 2 different brands? or is it another trip to the home center?
If it didn't leak the problem might not be the tank. Did you check the float in the tank to make sure it's adjusted to let a high enough level of water in?