Chat - Why is it Chat lite when I installed Chat Full

What is the deal? I installed Chat on our website http://glutenfreeworks.com. It shows up as Chat full on the site. When I tried to add it to a page http://glutenfreeworks.com/nutrition-testing it showed up as Chat Lite. When I looked at the plugins, it is listed as Chat Lite - No Chat Full is listed.

When I tried to re-upload Chat, I couldn't do so as I was told the file existed.

What is going on?