First off, you're right - any image on a computer screen is technically a digital image. I've seen good and bad B&W, whether it was digital capture, traditional film, color neg printed B&W, scanned film, wet print...

My two cents - when I think B&W, I usually think of a look like Tri-X which has some grain to it. It's nowhere near as clean as a DSLR at ISO100; ISO800 gets a little closer to that look, but it's not quite the same thing. Not that any one way is necessarily better than any other - just my preference for B&W is film and silver print. I don't have a darkroom so most of what I do is either scanned film or digital capture but if I had the time and space I'd probably do my own wet prints to get that look.