Comment by tjohns

FileMarker Pro had a dedicated server product (FileMaker Server) that you could use for multi-user access. Claris still sells it: https://www.claris.com/filemaker/

Microsoft Access was strictly file based. You could drop the .mdb/.accdb file on a SMB share and it would support basic concurrency via lock files. However, you could also swap out the internal database engine (Jet) with anything else via ODBC, so your Access database could connect to a remote Microsoft SQL Server instance - or even MySQL/Postgres.

Back in high school, I even wired up an Access database to give a graphical frontend to an accounting app running on an IBM AS/400 mainframe. ODBC made it easy, and Access itself didn't really care where the data lived.