My Media 

My Media is a repository of a single user’s media, where each user has a personal searchable repository for viewing and managing private media content. 

Users with a Teacher, TA, or Course Designer role in Canvas can embed media from My Media in rich content editors or add as Module items. The My Media button can be enabled in the Canvas course navigation menu and is also available in Account > Profile > My Media.

Media Gallery 

The Media Gallery is a searchable gallery of media content of a specific course. The Media Gallery is intended to be used as a media syllabus for a course, as a social media repository of the course or in some cases for media assignments. 

The Media Gallery does not necessarily include all media that is used within the course in other contexts. Instead, the Media Gallery contains the content that was deliberately assigned to it. The Media Gallery button can be enabled in the Canvas course navigation menu.