A story is a dynamic node that focuses on something current or topical, and isn't very long-lived. It goes into the archive, but it's not expected to be relevant for very long. When in doubt, a story is probably what you want.
Stories show up in the Recent Stories news feed.
Events are for items that have a date and a location; those fields are given prominence in the template, and used to filter them in the events calendar.
A page is a static node, with content that doesn't change very often. It's expected to be very long-lived.
Pages don't show up in the Recent Stories feed.
This is where you add items to the home page slider. If you're linking to a story, you'll need to create the story first.
This page shows all the content on the site. You may first need to click on the 'reset' button to show all content.
To show all Home Page Slider Items, click on the 'type' button, then pull the menu to it's right down to 'Home Page Slider', then click filter. From here you can edit or delete the items.