Bags with two straps, intended to be worn on the back:
backpack — medium size, often used in school and university, with lots of pockets and compartments
string backpack — small, inexpensive, usually with zero or one pocket
backpack purse — smaller, higher-quality materials with a greater focus on aesthetic construction
hiking backpack — very large, waterproof but often with some exterior pockets, light-weight construction (e.g. Cordura, silnylon), designed for carrying a heavy load over long distances, and usually has a hip belt to distribute the load
Bags with a cross-body strap:
duffle bag — large, and has minimal pockets/compartments, preferring to have a single large compartment for gym clothes and shoes
bicycle messenger bag — large, with many interior pockets similar to a backpack; when designed for actual use on a bike, they're extremely waterproof (with a single flap and usually zero exterior pockets)
messenger bag — intended for more casual use not on a bicycle, often less waterproof than the original version
vertical messenger bag — like a regular messenger bag, except like the portrait/landscape switch
military duffle bag — extremely large, constructed of heavy canvas, usually waterproof, and sometimes has a set of backpack straps along with a cross-body strap
cross-body purse — smaller, higher-quality materials with a greater focus on aesthetic construction