Logitech is a bit iffy also lol. But I can only assume that it puts it in to hibernation/sleep mode if it booted straight to where you left off.I am in the process of knocking up a SFF PC for my good lady and I have a Logitech wireless mouse/KB so will have a look later once I have it installed. At the moment I am waiting on a case for the build so the parts though connected are in a bit of a mess at the moment. Just installed Windows so will update then install the mouse/Kb and let you know.
Almost certainly a sleep button, not power off / on.
This will put run down the disks and generally put the system in to a low power state, but maintain the memory. When you went to power-up, it would have just restored the full power ready for you to carry on from where you left off. Note that if you had subsequently fully powered off (whilst in sleep mode) the memory contents would have been lost - whether you would have lost any work or not would have depended on whether you had saved to disk and the caches had been flushed.