Do non-PostgreSQL database softwares use roughly the same "structure" for communicating with them?
Most client/servers DBMSes have parameters similar to those, and the handle database indeed is an unknown concept elsewhere. But they might need other parameters; the common way to handle is with a connection string (or URL) that encodes all those parameters, or with a generic list of keys/values.
And for databases that do not use a client/server architecture, it's even more different. If you do not need much concurrency and want to avoid having to install the DB server, you would be likely to choose SQLite, and then the only connection parameter is the database file name.