Not an expert by any means, but the K bikes are inlines, usually I4's I believe, and the R bikes are Horizonally opposed 2 cyl's. The classic BMW look with the cyl's poking out the side are R Bikes, although the newer R's are oil/air cooled while the older BMW's are just air cooled.
The K Bikes, I believe, are water cooled.
BTW, if someone else offers info that contradicts me, I'd tend to believe them. As I mentioned, I'm no expert, just an R bike fan.