Many people get them confused with each other. They are similar, but they are also different. Asterisms are groups of stars that make a shape or form of something. The Big Dipper is an example of an asterism. It is made of seven stars, four make up the bowl and three are the handle.
Constellations are a group of stars that often include asterisms.
They are usually outlined by some imaginary line for them to have a shape. The Big Dipper is an asterism in the constellation Ursa Major. Often it is easier to find the asterism in the constellation than it is to find the constellation itself. For instance, I can find the Big Dipper very easily. Once I find the Big Dipper, then I can see Ursa Major.