Task: Task that needs to be done. Task is a unit of work contained within a story. In JIRA Agile, individual tasks are represented as sub-task issues, and stories are represented as (parent) issues.
Sub-task: Smaller task within a larger piece of work. Sub-tasks are ones generally used to split up a parent task into a number of tasks which can be assigned and tracked separately in a project.
Story: Functionality request expressed from the perspective of the user. User story is a software system requirement that is expressed in a few short sentences, ideally using non-technical language. In JIRA Agile, a story is represented as an issue, and individual tasks within the story are represented as sub-tasks.
Bug: Problem that impairs product or service functionality.
Epic: Large piece of work that encompasses many issues. It is essentially a large user story that can be broken down into a number of smaller stories. It may take several sprints to complete an epic. In JIRA Agile, an epic is simply an issue of type "Epic", with which other issues can be linked.
Incident: System outage.
Service Request: General request from a user for a product or service.
Change: Roll out of new technologies or solutions.
Problem: Track underlying causes of incidents.