Oxford English Dictionary Argument (noun) 3a. A statement or fact advanced for the purpose of influencing the mind; a reason urged in support of a proposition.
4. A connected series of statements or reasons intended to establish a position (and, hence, to refute the opposite); a process of reasoning; argumentation. (Argumentation 3. A sequence or chain of arguments, a process of reasoning.)
5a. Statement of the reasons for and against a proposition; discussion of a question; debate.
7. The summary or abstract of the subject matter of a book; a syllabus; fig. the contents.
Argue (verb) 4a.intr. To bring forward reasons concerning a matter in debate; to make statements or adduce facts for the purpose of establishing or refuting a proposition; to discuss; to reason.
b.Hence, To reason in opposition, raise objections, contend, dispute.
5.trans. To bring forward the reasons for or against (a proposition, etc.); to discuss the pros and cons of; to treat by reasoning, examine controversially.
9.to argue (a person) into or out of : to persuade him by argument into, or out of, a course of action, an opinion or intention.
The argumentative essay is a genre of writing that requires the student to investigate a topic; collect, generate, and evaluate evidence; and establish a position on the topic in a concise manner. (https://owl.english.purdue.edu/owl/resource/685/05/)
A critical essay is an argumentative piece of writing, aimed at presenting objective analysis of the subject matter, narrowed down to a single topic. The main idea of all the criticism is to provide an opinion either of positive or negative implication. As such, a critical essay requires research and analysis, strong internal logic and sharp structure. Each argument should be supported with sufficient evidence, relevant to the point. (Wikipedia)