The File System
(Tools & Administration > Files) is for an internal administration of files
of all kinds, e.g. the portal stores neccessary SEO files (Search Engine Optimization) automatically. Images needed for the layout of the portal or placed in stories are saved in the files system as well.
The Document Management System
is for public provision of documents
or files. That means that your employees, partners or customers can - depending on their access rights - access the DMS on the portal surface with its folders and files and download and save the files.