"Under the Apple logo drop-down menu (at the top left of screen),
there is the selection SLEEP.
What EXACTLY does this SLEEP selection do."
When Sleep is functioning properly, this should sleep your display, your Mac Mini, and some attached peripherals (where relevant), according to your settings in the System Preferences/Energy Saver panel. Its behavior should mimic your timed sleep setting in Energy Saver, but just do it right now.
"Does it Sleep the M1 Mac mini only?
Does it Sleep the Studio Display only?
Does it sleep BOTH the M1 Mac mini AND the Studio Display?"
By default, it will put both to sleep. If you check the box for "Prevent your Mac from automatically sleeping when the display is off" it will only sleep your display. I am not aware of a way to sleep the CPU w/o sleeping the display.
"Does this Sleep selection do the same thing as the Energy Saver Sleep OFF timer?"
Yes, except it does it right then when you select the menu item, rather than after 10" (or whatever) of user inactivity.
"What is the difference between the manual Sleep selection and the Sleep timer?"
Simply that the menu item sleeps right now rather than after a set amount of user inactivity.
"Is one of these SLEEP controls better than the other?"
The timer is good because you never know when the minute interruption could turn into an hours interruption. But if you know you're going to lunch, put it to sleep now.
Sleep was a bigger issue in the days of CRT displays and CPU's whose fans were louder than my air conditioner. CRT displays left with the same image on them for too long could actually have the image permanently "burned" into the display. Both displays and CPU's used much more energy than modern M1 Macs and solid-state displays. Nonetheless, they do use energy. Depending on your particular peripherals, when your Mac sleeps, it may also turn off fans and power to the peripherals.
I have no experience with M1 Mac Mini sleep, but my Mac Studio's sleep behavior (and a lot of others, it seems) is currently erratic, to put it mildly. This could be adding to your confusion. Allegedly Apple is aware of the issue.
