The demoscene started out of the software piracy scene. An intro was a short thing like this one, that people put into the boot sequence of games they cracked or otherwise made available to the scene. Over time these got more elaborate and people started making them separate from the games to show off their prowess in coding, called demos. Nowadays the names serve to differentiate the runtime length and size of the program. Intro = short thing, demo = long full effort thing.
> Intro = short thing, demo = long full effort thing.
The problem is that that's not true anymore either. Many intros are equally "long full effort" as your average demo. Intro simply means "demo with a size limit", these days (and by "these days" i mean "the last 15 years")