What is the difference between a hotel and a bed & breakfast?

A bed and breakfast (or B&B) is a small lodging establishment that offers overnight accommodation and breakfast, but usually does not offer other meals. Typically, bed and breakfasts are private homes with fewer than 10 bedrooms available for commercial use.
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Motels are a type of hotel for motorists. Typically, you can park directly outside of the hotel room. Hotels are often more upscale from a motel, even though they range from economy to luxury.

A bed and breakfast is usually located in a former residential home, with a home-like atmosphere. Each room is generally decorated differently, and you may have to share a bathroom with other guests. Breakfast is served in a dining room, but it’s not a restaurant.

Hotels tend to be much larger commercial buildings, with a more industrial feel. Each room is generally identical to the next, with its own private bathroom. Many hotels include a full service restaurant.

A hotel accepts most paying guests, a bed & breakfast is known to refuse homosexual couples on principle.

About $100 a night.

But to elaborate:
Most hotels are in commercially zoned areas. Most B&Bs are in areas zoned for residences, so the neighborhood feel will be different.

Most hotels (other than the budget ones) have a bar and restaurant attached, and most B&Bs have announced hours for “breakfast only” (maybe a box lunch, too, if you’re lucky) in a dining room, and no liquor (or liquor license).

Most hotels have a full wait staff, and most B&Bs have a bare-bones cleaning staff that you probably won’t even see.

B&Bs are good if you want a laid-back, friendly experience. Usually the staff and other guests are friendly and somewhat sociable. Often they’ll have an evening reception or social hour, with snacks and wine or something, along with breakfast. B&Bs are also generally quieter and nicer (a home-like way) than hotels. They can be expensive, but they can also be cheaper than a typical hotel. It just depends on the area and the particular B&B.