Screensaver seems to be permanent; thus presumably harming the screen.
I selected "sleep" on my iMac, unplugged the Mouse and turned off the keyboard and shortly after the screen was active; can't recall whether the screensaver msg. was there immediately or a while later. I waited for a few minutes and the screensaver msg. didn't disappear. I've checked under Sys. Prefs. and there is no option regarding timing (apart from how long before the screensaver activates) so two questions: Is the "screensaver" an obsolete term which really means screen degrader and if used does it ever turn off and/or is there some setting to arrange that?