I've tried to do a little research on my own to answer this question. Perhaps some of you who are more familiar can confirm or expand.
It looks like there are two levels of small footprint implementations. There appear to be "micro" implementations that sound like a Windows clean boot--bare bones OS that can be used for things like operating a Raspberry Pi or simple tablet, or booting off a flash drive to do maintenance and repair. These don't appear to have much in the way of a software library. They remind me of the Sinclair computer. Some people managed to hang a lot of peripherals off them and actually do something, but they were never intended to be a serious office machine.
The other are "lightweight" packages that look like something someone might use as an XP replacement on an older computer with limited hardware resources. It looks like these contain all of the necessary pieces to be a full-fledged OS, particularly if your needs are basic. If I understand what I'm reading, they save weight in a couple of ways. The "full-sized" implementations come with a hefty software bundle so they are ready to replace Windows for the typical applications most people run--full-featured replacements for MS Office, Outlook, Photoshop, etc. The lightweight ones come with lightweight software and less of it, sort of the equivalent of Microsoft Works instead of Office. The other difference I'm seeing is a bare-bones user interface--a very simple desktop.
Does that accurately sum it up? Many of the reviews I read recommend Puppy Linux as the best replacement for XP on an old machine. Any differing thoughts or recommendations?