It's hard to put a label on what that diagram is called but you are essentially looking to visualize the flow. This can be called a 'flowchart', 'user flow', 'UI flow', or a ux 'use case' (different from a programmers 'use case').

A good example of a flowchart can be found here: 

https://www.lucidchart.com/documents/edit/4543-dcc8-5123936c-8c53-10720a005798#?demo=on

And a good article about a quicker way to sketch this out can be found here: 

http://37signals.com/svn/posts/1926-a-shorthand-for-designing-ui-flows

I don't think it really matters what diagram you use, what is important is that you can visualize what needs to be done and get everyone on the same page. I personally prefer a flowchart because it has well defined symbols that create a standardized language to convey the necessary steps for designers, project leaders, programmers, and the likes. Either way, for registration, I think the conditional is an important aspect for showing what decisions the user will have to make and where that will lead them. Also remember that some conditionals will be decided by logic not the user.

What kind of diagram is best to represent the flow of a registration process?
As someone whose still new to agile, I'm not sure I completely understand the relationship or difference between a user story, feature, and epic.

According to this question, a feature is a collection of stories.  One of the answers suggest that a feature is actually an epic.  

So are features and epics considered the same thing, which is basically a collection of related user stories?

Our project manager insists that there's a hierarchical structure:

Epic -> Features -> User stories

... basically all user stories must fall within this structure.  Therefore all user stories must fall under an umbrella feature and all features must fall under an epic.

To me, that sounds awkward.  Can someone please clarify how user stories, features, and epics are related?  Or is there an article that clearly outlines the differences?
