Oh, yes, that's quite possible.
In my "Devices and Printers" panel, for some reason I have an entry for both "PLAYSTATION(R) 3 Controller" and "Xbox 360 Controller for Windows". Right-clicking either one of them and selecting "Game controller settings" brings up a dialog with an entry for "Controller (XBOX 360 For Windows)". Does that resemble what you are seeing at all?
January 19, 2018, 01:34:31 am - (Auto Merged - Double Posts are not allowed before 7 days.)
I should add that if you are using the stable release from January 2016, apparently the beta is significantly different. Alternatively, if you're using the beta, maybe the stable release would be better? Just make sure you follow the instructions about wiping the old install if you switch from one to the other.