Back in the day, I would power off my hardware. My computer would tell me when it was safe to power off, my Genesis and PS1 you pressed the power button and that was it.
But when I got my PS2, turning it off wasn't just turning it off. The power button didn't turn anything off, it just reset the system. So I always hit the power switch on the back.
It wouldn't be for a while before we learned we can turn it off and back on faster by pressing and holding the power button. Rather than killing the system. And newer systems like the PS3 didn't like it at all when they were powered off completely.