There is definitely a connection twixt the two, but there's an interesting historical tidbit that could probably stand some investigation, particularly the language aspects.
I grew up in the then-small town of Burke, (Fairfax County) Virginia, hard by the main line of the Southern RR. Not 3 miles south, there was a crossing called Sideburn Crossing, where stood a very old hotel. And there exists a picture of President Lincoln taken in front of that very hotel, with the sign Sideburn Hotel in the background, I believe. Anyway, that crossing was known as Sideburn in the 1860s, and I have always wondered if there were a connection between that location and General Burnsides. Hardly seems likely, but certainly an odd coincidence.
In 1962 or so, our local fire department burned that hotel as a drill! In retrospect an historical tragedy. Somewhere I have pictures of myself as a very young volunteer standing beside the hotel just before we set it on fire. Clearly visible behind me are the drinking fountains labeled "White" and "Colored." Not visible, but definitely there, were the construction beams, mostly oak, but some chestnut, twelve inches square and 40 feet or so long that formed the skeleton on the building. I cry when I think of the many uses for that wood other than to teach us how to wet down the ruins, which is pretty much all our fire department was good for at the time. Not to mention the lost historical value.