When both terms are used in the sense of being parts of something else, they have different meanings. Cars are made of many components. You can take a car apart and have a distinct individual component which can be used in another car. Cakes are made up of many constituent items. Sugar is one constituent. After you bake a cake, you might be able to detect that it is sweet because of the sugar, but you will never be able to unbake the cake to get the sugar. The individual constituents form an indivisable part of the whole.

These are the same when you are using it as an adjective. However, when it is used as a noun, constituent means a person who is represented by or authorizes another, especially in politics. A component when used as a noun is almost never a person, but usually a part of a machine or electronic device.