Would depend on the chamber of the revolver. As far as I know, there are only three mainstream revolvers in the history of 10mm. Look inside the chambers themselves and if there is a ridge where the front of the case mouth headspaces, then you should not chamber .40's in there unless you don't care about messing up your chambers.
The three revolvers I'm thinking of are the classic 610 by S&W, the new Nightguard from S&W and the Buckeye Convertible special edition .38-40/10mm Ruger Blackhawk.
The new S&W night guard is advertised as a 10mm/.40 S&W, so I'd say yes for that one. I'd say NO to the Buckeye Blackhawk, as it's not made for use with half or full moon clips. The 610, probably, but someone else will have to weigh in on that.
As for the difference between the two calibers-- it's slight. Same pressure, shorter COAL for the .40, obviously, but the same external circumference of a loaded round.
So if the question simply is, "will a 10mm revolver chamber a .40?" then the answer is absolutely that it will, but for some of them, NO-- you certainly should not do it and it could harm the handgun.
In a semi-auto, you'd have the same damage to the chamber and whether or not it would fire would depend on whether or not the extractor managed to hang on to the loaded round well enough to absorb the chambering and the firing pin hit.
When you are talking about rimless or semi-rimmed pistol calibers, it's not like rimmed revolver calibers that headspace at the rim. .38 in .357, sure, but you can't do the same with .40 and 10mm unless you want the possibility of chamber damage.