ETT is affected by seat tube angle, reach is not
Well, no, the three are inter-related. If you keep ETT constant and vary seat angle you change the reach. Keep the reach constant and vary the seat angle and? you change the ETT.
Stack has an effect as well: adding spacers under the stem effectively reduces reach and (to a lesser extent) ETT. So if you end up looking at a frame with the right reach but the front end is too low for you then it ends up being equivalent to a frame with the right stack but too small a reach.
Also, adjusting saddle fore/aft position is like adjusting seat angle and ETT, but has no effect on reach. With a road bike that’s determined solely by physiological parameters, but on an MTB weight distribution comes into play.
But yes, reach for standing and ETT for sitting is roughly on the money.