Zotero can serve as a PDF management application. It can download PDF files along with the metadata of the references, and you can find them and search their contents in Zotero. If you use Zotero to store files, it is a good idea to keep an eye on your storage space (300MB).
Log in to your account at zotero.org → go to Upgrade storage.
Or go to your account Home → Settings → Storage.
To enable Zotero to automatically download PDF files when you import a reference, or to prevent this being done, go to Edit → Settings → General → under File Handling, check/uncheck Automatically attach associated PDFs and other files when saving items.
If you are using a Mac, you can find this setting via Zotero → Settings → General → check/uncheck Automatically attach associated PDFs and other files when saving sources.