[Technologist]

Moire occurs when there is interference between spatial frequencies of almost identical periodicity
(or octaves from identical) .... a form of aliasing
Thus (often) very small movement in camera and screen can cause it to come or go....
So if shooting a screen straight on is OK - it being 5 degrees off may not be
and of course zooming the camera changes the screens spatial frequency displayed on the sensor.
and likewise the moire comes and goes.

The softer/ out of focus the screen is helps matters - as the periodic pattern is less obvious.
there are also issue with the optical filtering the camera (Anti aliasing) - they are different -
and any down stream image hf enhancement .

The closer the pixel spacing on the screen makes it less likely to have Moire surprises
as is the further away the camera is......
but shooting obliquely can have all sort of strange effects!