The Theme section allows you to adjust overarching items that appear in the Theme such as social media links in the header or verbiage in the footer via the "Appearance" tab. You can also view the Asset Files (CSS, Images, JS) as well as the Templates (HTML) and Layout files (HTML) that were uploaded for the site in the "Files" tab.
The Appearance section is where you can edit items that appear on multiple pages or every page of your site. Things like Social media links in the header or a text block in the footer can be managed here (instead of on each and every page of the site). The management fields in the Appearance section will differ from Theme to Theme.
Page Templates are your HTML template files. These need to have GovTags applied in order for the Governor Content Management to be in place.
For more information on how GovTags work, see the Theme Documentation.
Site Asset files include CSS, JS, and Image files. Those files can be found and managed under the Site Assets section in Site Templates.
Layout files are the HTML files associated with your site. These could include Header and Footer files. They can be managed here.