My personal bet is on people placing that line squarely on the divide between "Stoic Guru" and "Active Academy" UX models[1]. An AI is probably, to most people, an agent that continues to think and learn when it is not being interacted with—by surfing the internet, maybe—such that it can generate novel outputs, and revise its own previous beliefs, with no user-visible step that would be perceived as "re-training." Something that will come to you with thoughts it has had that you'll find relevant, that were inspired by new data the agent has acquired not derived from your input.
A simple example that people would probably think of as "AI" (and which people wouldn't accept as a UX paradigm unless it was presented to them through an agent-based interface) would be a spam filter like GMail's that learns from the classifications of everyone who uses it, that would go back and reclassify messages that it now had a more refined opinion on. Nobody would want a dumb algorithm to take emails that "were" in their inbox and move them over into their spam folder—that's destructive!—but they'd accept a (virtual) secretary using their judgement to do so. Thus, AI.
[1] https://scifiinterfaces.wordpress.com/category/active-academ...
To put it another way, if we define a Scotsman as anyone born in Scotland and/or related to someone born in Scotland, we've essentially just defined a Scotsman as every organism ever to be alive on Earth.
I have to imagine when the term first started to be used people imagined an AI as something more human than neural networks. Imagine HAL or any other hollywood perceived robot.