How do I display a view pane with all items of a category? I created an Events content type.
I created a vocabulary that has two category terms, Events and Plays.

I have a view that contains a list of all content of type Events.

Each Events listing displays with the category term as the title/link.

The link should go to a page that has a content pane containing a list of all of the Events with that tag.

So, the view looks something like,

Movie (term)

movieName

movieTime

Play (term)

movieName

movieTime

Movie (term)

movieName

movieTime

Play (term)

movieName

movieTime

Movie (term)

movieName

movieTime

The term field is configured to be a link.

If I click on Movie or Play I want to go to a page that has a content pane containing a list of all of the Events tagged with Play or Movie, depending on which I clicked.

On the view, I set up a Contextual filter:

Content: Has taxonomy term ID

I set up a Relationship:

Content: Taxonomy terms on node

How can I set up this view so that clicking on the category will take me to another page with a view/content pane that displays a list of Events based on that tag?
First you will need to have the views page that displays all the Events for the tag you want, then it should be a matter to rewrite the Link field to output as a link that point to that page you had created.

FOR THE PAGE:


Create the page using views that will filter all Events with category Terror 
In the URL make it the exact TERM you will have in the list you need, i.e. www.yourwebsite.com/TERROR
Save


FOR THE LIST:


Create the block/page view you need with the list
You need to add the field TERM again (it should appear twice, one above the other, rearrange if not).
In the first TERM FIELD check the box for Exclude from display
On the second one, go to Rewrite Results > Output this field as a link, check that box
In the text field that appears, enter the replacement pattern for the first TERM FIELD, something like [field_term].


That will render your TERM as a link to the TERM page, that will contain all the events for that term. 
If not, place a link so I can help you.