Staging and Production with WordPress
Staff changes should happen on the live server.  This is doubly true if you have any public-facing pages, which will mean the database on the live server is updated by members of the public.

Traditionally, code travels from dev to staging to prod.  Data travels from live to dev/staging.

I prefer referring to "dev/test/live" server, since this better illustrates the flow, and is less jargon-y to non-tech staff.

Some changes don't flow well this way - for instance, you may want to create a contribution page on your test server, then transfer it to live.  In practice, this should be relatively infrequent, and you can redo your work on the live server.