Note: You are currently viewing documentation for Moodle 3.2. Up-to-date documentation for the latest stable version of Moodle is probably available here: Logos.
The settings in Logos in Site administration are for defining two variants of a logo to be used as part of the interface for your site.
These settings were only added in Moodle 3.2 and were intended to allow a basic branding of the site to be independent of the theme used, so that multiple themes could be used or tried without having to set the logo again in each one.
A full logo to be used as decoration by some themes (such as core themes). This image can be quite high resolution because it will be scaled down for use (and cached for performance). Logos that are wider than they are high usually give better results. Formats accepted: PNG and JPG.
A compact version of the same logo as above, such as an emblem, shield or icon. The image should be clear even at small sizes. Formats accepted: PNG and JPG.