A motel (in the US, at least) provides individual, self-contained rooms for travelers. Each room has a minimum of accoutrements: heating, air-conditioning, bathroom including bathtub, shower and toilet, and television. Most rooms go beyond that and have radios, coffee makers, ironing boards and irons, hair dryers, etc. Many motels (but not all) offer a breakfast buffet that is included in the price of the room. The breakfast is usually continental, and consists of cereals, omelettes, frozen waffles, yogurt, fruits, toast, muffins, bagels, coffee, tea and juice.
A bed and breakfast is a room for rent in someone's home. It is not self-contained - that is, you'll have to walk through part of their house in order to get to your own room, unlike a motel - and not all rooms have private baths en suite. Nor do they necessarily have in-room thermostats for the heating and air-conditioning. The breakfast offered is usually a bit more elaborate that the buffet available in motels; most bed and breakfasts have things such as bacon, sausage or ham on the menu as well as eggs cooked to your specifications (fried, scrambled, poached, etc.).