I'd say an important identifying detail of Hybrid is having moderate width road bike tires on road bike sized wheels, ie. 700c these days. Perhaps another characteristic is a crank with 28, 38, and 48 tooth rings and a wide range cassette. In other words, rings bigger than a MTB but smaller than a road bike.
Of course a small frame Hybrid might use 26 inch wheels, though that seems rare.
A "true" flat bar road bike would have a full road bike drive train with just the flat bar instead of drops. I think someone here bought a bike like this recently...
As for a rigid 26er bike with skinny tires... they seem generally not to be produced new. Perhaps there are too many old MTB's that can be converted thusly. To the extent that such bikes are sold, I think they might be labeled as "urban" bikes.




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