I may be wrong, but I don’t know that anyone ever tried to answer this question. Your statement seems to be as accurate as anything I have read in the “Complete Idiot’s Guide to Motorcycles” or in other books. There are more bikes than definitions. See Sport-Touring, Enduro, Adventure, Dual Sport (etcetera ad nauseum).
It might, perhaps, to be more accurate to say that a café racer was a street bike, decorated and customized to look like a racing bike, but was primarily aimed at display to others for bragging rights at the local bar or coffee shop. Triumph makes an “upright” bike, designed to be ridden by a rider way forward hugging the tank. Real sport bikes are, at the extreme, street legal rocket ships which are racing bikes. I’ll leave it to others to decide if a sporty looking bike with less threatening power should be called. I mean, what is the Kawasaki 650R, or the Suzuki SVs?
Warning: the preceding was my best guess based on reading. I wouldn’t be surprised if I were wrong, or offended if someone has better information.
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