STATIC_FILES and MEDIA_FILES are two different things, and should reside in two different directories. The collectstatic command has nothing to do with media files.
To make media files available, you need to ensure your webserver is configured to serve the directory where those files are stored (MEDIA_ROOT), and the urls are generated using the url attribute of the filefield object and not using the static tag. (See Model field reference | Django documentation | Django and the examples at Managing files | Django documentation | Django)