What's the difference between Beaver Builder Theme and Beaver Themer?

Beaver Builder Theme is a WordPress theme. Beaver Builder Plugin (Page Builder) and Beaver Themer (Theme Builder) are both plugins.

Every WordPress installation requires a theme. Themes control the header and footer on the page, as well as options such as a sidebar or footer for widgets and how blog posts are displayed. 

Page Builder (the Beaver Builder Plugin) lets you easily create layouts in the content area of the page. That's the part of the page that is not controlled by a theme.

Theme Builder (the Beaver Themer plugin) helps you create theme layouts to control everywhere on the page except the content area. Theme Builder requires Page Builder to construct the theme layouts, but they apply to areas of the page that are outside the content area.

Which of the three Beaver Builder products do you need? 

The Beaver Builder plugin is the base product for content layouts. It works with most themes and does not require the Beaver Builder Theme. 

The Beaver Builder Theme is a well-coded framework theme that is tightly integrated with the Beaver Builder plugin. Beaver Beaver plugin plus Beaver Builder Theme give you enough flexibility that you'll probably never have to buy another theme.

If you're a more advanced user and you want to style your own theme areas or add a spectacular layout to your Post pages, then Beaver Themer is the add-on to get. It requires the Beaver Builder plugin, but it doesn't require the Beaver Builder Theme, even though the two are designed to integrate well with each other. See the  list of themes that are fully supported by Beaver Themer.