My understanding is that facing is machining (by hand usually) the
ends of the BB housing and top/bottom of the head tube where the
BB retention nuts and headset bearing cups fit to that the fit is
close to exact with no high points or irregularities to the surface.
Properly faced the surfaces are flat and parallel and at right angles to
the long axis of the cylinder.
Chasing is running a tap through the threads after facing so that the
threads are clean.