The other Michael Brophy (PA 114) enlisted in Philadelphia; according to HDS, his residence was Tacony (Tacony is a part of Philadelphia). Nottingham is only 55 miles or so from Philadelphia (whereas Nottingham is nearly 197 miles from Scranton).As far as his enlistment goes I have records from 1863 and 1864. I thought it might have been a typo but what you say is possible, he could have registered one year and then enlisted the next. I'm not sure if there was a draft - maybe he had to register and then didn't get drafted until the next year? That could open up some more possibilities. I could search for records around both Scranton and Nottingham. Maybe knowing the area could give me more clues. I've been through the PA and National archives but if I can narrow it down to a city or county I might get better information.
In Maine, if a man who registered for the draft was called up, that information was often recorded under the Comments column. The only comment on the Nottingham registration regarded his having filed a naturalization intention.
When your Michael Brophy (PA 45) enlisted, he was a substitute--and that certainly sounds like something coming out of the draft of the previous year. If he is not the Nottingham man, someone else registered (probably in Scranton area), was called up, and paid your MB to go in his place.
There is a Michael Brophy in Philadelphia on the 1860 census--but a younger man. There's another MB in Erie County (out by Pittsburg)--but he is older. However, there are 3 different men, named Michael Brophy, in New York City.
Going through archives online may not be the route to go in such a complicated case. Online or in-person, archivists and librarians are our friends. I'd contact both archives (each should have a contact link for assistance). Or, on this list is Bob Velke, a registered vendor (I believe that he does research into this kind of thing at NARA--but I don't know his fee schedule). He may be a good person to set to work on this--or simply to be a knowledgeable sounding board re NARA records.