UnHosted or 0Data are names for WebApps where the app. creator doesn't (and doesn't presume to) hold your data.

Remote Storage is a protocol for apps that run in the browser to talk to a back-end run by someone else, where users have a choice between back-end servers.

https://remotestorage.io/

An example RemoteStorage server in PHP : https://github.com/fkooman/php-remote-storage