Hm. Easiest way to think about it is size and what services they offer. As an American, when I think of an Inn, I think of an old Renaissance style pub or bar with a couple of bedrooms upstairs for travelers. I don’t think many Americans would consider is to even have Inns as a service industry since they are small and attached to a bar. I’m not sure we have hostels much either. In Europe, the hostels I stayed at might offer someone a bed in a room or hallways with many others. The bed could be very small and built into the wall. Think like a boarding school or military barracks. The bed is cheap and designed for backpack travelers and such. Hotels in American can be very luxurious. They cost a lot more and often have swimming pools, nice food, maybe a small gym in the building. They are close to business areas and are often for vacation. America also has motels. They are like hotels but smaller, usually a bit cheaper and are near highways. They don’t usually offer swimming pools or maybe just a very small breakfast. They are for overnight travelers, not vacationers.