Linking a media object displays it as the file rather than an icon
PDF files will be displayed in the media record regardless of whether they are linked or embedded. Embedding a document actually adds the file to the database files, and it is stored as a part of the database. When it is linked, it will not be added as a file in the database.
To see the file as an icon, choose the option to link the file and then mark the option to display as an icon. This will prevent the data from being included in database but will still show the file as an icon.