I'm not intimately familiar with TFS, but in Scrum terminology, a requirement is one thing that may be a Product Backlog Item.
Consider the following from the Scrum Guide:
The Product Backlog lists all features, functions, requirements, enhancements, and fixes that constitute the changes to be made to the product in future releases. Product Backlog items have the attributes of a description, order, estimate and value.
If the Product Backlog contains only Product Backlog Items, then a requirement is one type of Product Backlog Item. A bug report would be another. A refactoring task could be another. Technical debt paydown would be yet another.
"Epics" and "Features" aren't a part of Scrum, as defined in the Scrum Guide. An Epic (and sometimes a Theme) are ways to group User Stories. The Scrum Guide doesn't require User Stories (it's mostly silent on how to format Product Backlog Items), but many teams have found success with them. If a Product Backlog Item is a User Story, it may be part of a larger Theme or Epic that describes a particular flow through the system. However, a Theme or Epic may not be something that is reasonably deliverable within an iteration.
In your case, requirements would be captured as Product Backlog Items. You may or may not want to group Product Backlog Items into Features or Epics - it depends specifically on the way you and your team decide to work.