Constellations are the 88 recognized patterns and groups of stars. These groups and patterns are usually associated with mythology. Today, constellations are not only the groups of stars, but now refers to the entire region of the sky that it takes up.
Asterisms are groups of stars that do not form their own constellations, but instead, are inside of constellations. The Big Dipper is an example of this. The Big Dipper is an asterism inside of the constellation Ursa Major. So I believe that asterisms are smaller than the constellations that they're in, but not necessarily bigger than all constellations.
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