It seems that any bike designed for the road that has a flat bar is given the moniker "hybrid" --although it might share every other characteristic with actual road bikes.

For rough roads, a mountain bike is a good choice when it is a hard-tail. For off-road, a mountain bike is the best tool for the job.

There used to be a classification of road bike that was not a comfort bike, not a racing bike, not a cruiser, but, was good for around town... cross-trainer. It was a forerunner to the hybrid with mid-sized tires (road) for better comfort. I bought my son a Raleigh cross-trainer years ago. Unfortunately, comfort bikes took that market-share and the cross-trainers have disappeared.