Why does the 3DS talk about Sleep Mode when you press the Power Button?

Question

When I press the Power Button once on my 3DS when turned on, I get a screen about Sleep Mode. It tells me I need to close the screen to enter Sleep Mode, insinuating that simply closing the 3DS when not on this screen, won't activate Sleep Mode.
So what happens when I just close the system when playing a game? Is that not Sleep Mode? If it is, then why the talk about Sleep Mode when I press the Power Button?
I can sort of skip that screen by holding the Power button down for a second or two, but the entire notion of that screen just seems silly to me. I wish I could just turn off the system with a single short press of the button.

Answer 1

It's just poor copywriting. Closing the 3DS in a game includes all the features listed except that street pass is not enabled when in a DS game (3DS games still allow streetpass when sleeping), so you certainly don't have to enter the home screen just to put it to sleep.

That screen itself is just a tutorial to teach you that you don't have to press the button to do that; you just close the device. You can close the device on the home screen (not the power button screen) and streetpass remains active.

Answer 2

There is essentially no difference between closing the screen to put it into sleep mode or the power button sleep mode. You will have to think of this as a standby mode, just like that of a PC. It will turn off unneeded hardware or put them in a low-energy mode (CPU, screen, etc), but will keep up power to the RAM, resulting in you beeing able to continue your game from the point where you close your screen.

Sleep mode will continue to consume battery life until you turn off your device, and if you haven't saved and your battery dies, you will have to replay from your last save.
Turning your device off will help save battery power, if you don't want to use your 3DS for extended periods of time (e.g. ~3 hours or more).