In my apt the tapping noise can come from my ceiling or one of the
walls. When the tapping got bad a few weeks ago, it got bad in both
places at once. Why would that happen, if the problem is due to the
pipes rubbing against the holders?

Sometimes the noise is in one of the two places and sometimes it's in
both.

Someone mentioned a pressure regulator. What is that exactly, and how
might it cause the tapping problem?