Answer: there are different types of compositions like narrative, expository, descriptive, persuasive and argumentative etc.
Explanation: So firstly ,
1) Narrative: a narrative is form of writing that tells a story. narratives can be essays , fairy tales, movies and jokes . Narratives have five elements : plot , setting, character, conflict and theme.
2) expository: an expository essay is a genre of writing which tends to explain ,illustrate, clarify or explicate something in a way that it become clear for readers. therefore it could be a investigation, evaluation, or even argumentation about an idea for clarification.
3) Descriptive: the descriptive essay is a genre of essay that asks the student to describe something ,object ,person, place, experience, emotion, situation etc.
4) Persuasive: a persuasive essay also known as an argumentative essay is a piece of academic writing where you use logic and reason to show that your point of view is more legitimate than any other. You must expose clear arguments and support them by convincing facts and logical reasons.