Bitwarden is (primarily) a single db synced between devices via a server. A copy is kept locally on each device you sign into.
Changes made to an offline copy will sync to the server and your other devices once back online. (with the most recent change to each individual item being kept if there are multiple changes across several devices)
/edit: the local copy is for access to your passwords offline. Edits must be made with a connection to the server your account resides on, be that bitwardens or your own.
If you host your own sync server via vaultwarden, you can easily maintain multiple databases (called vaults) either with multiple accounts, or with a single account and the organizations feature. (options for creating vaults separate from your main one and sharing those vaults with multiple accounts) You can do this with regular bitwarden as well, but have to pay for the privilege.
Using vaultwarden also gives you all the paid features of bitwarden for free (as it's self-hosted instead of using public servers)
I've been incredibly happy with it after setting it up ~3 months ago. Worth looking into.