An argumentative essay tends to be a longer essay involving independent research, and aims to make an original argument about a topic. ... An expository essay also aims to be objective, but it doesn't have to make an original argument. Rather, it aims to explain something (e.g., a process or idea) in a clear, concise way.
Exposition is exposing, explaining, clarifying, proving, illustrating. ... Exposition's purpose also differs from argumentation, which is to persuade, convince, to change another's viewpoint or opinion or thinking, often to yours.