Sorry if I mixed up the links.
No, you only need an app, you don’t have to install any database. Personally I use MacPass (GitHub page), and on the iPhone currently MiniKeePass.
Alternatives for macOS are KeepassXC and KeePassX.
If you scroll down on this page, you find a more comprehensive list of “Contributed/Unofficial KeePass Ports” for all platforms.
kdbx (or the older version 1 kdb) is just the database format that is used by these apps. The format is platform independent. kdbx is also the filename extension for the database files.