Yes, it is possible to export just the attachments or just the files. There are no download limits; you can download up to 5TB of data or more than that in batches.
Follow the below Steps:
1. Open the "Mass File Download" application.
2. Select the subtab "Related Files & Attachments"
3. In the "Select Object" section, choose "Attachment", then hit the "Search" button.
4. All of your org attachments will display in the table below, which you can download in batches of "2000".