Short answer: The fine art/illustration divide is basically bullshit about enforcing class barriers.
Long answer: When I was working on the Gravity’s Rainbow pictures (a picture for every page of Thomas Pynchon’s novel) I found that there were some jobs a picture called an “illustration” was expected to do that a picture just called art didn’t have to do much in the same way that there are things a sculpture called a “chair” has to do that a sculpture just called a sculpture doesn’t have to do.
And, basically, the commercial category of “art” was developed, historically, (if you’re being charitable) as a place to put things that couldn’t be sold any other way. If you make a really nice jar it’s still a jar. If you make a really nice jar with a hole in the bottom then you have to call it art because you have no other choice–nobody’s gonna buy it to use it as a jar, all the soup’s gonna dribble out the bottom. Likewise, if it’s really ugly and boring but it definitely holds things, you can still sell it as a jar.
So, anyway: the category “illustration” means “this object can do a certain job for people even if it’s not worth looking at on its own”. The category “art” means “it is worth looking at whether or not it does the job”. Taking on both jobs is a rare challenge, like making a thing that is both chair and sculpture–but it can be done.
The oddest thing is, layered on top of this fairly understandable division, there’s an entirely shitty class-based division which began to occur once certain kinds of illustration became popular with young and/or not-rich people: Rich people needed to be assured that the very expensive objects they were buying were different than the cheap reproduced things that poor people bought to decorate or enrich their lives. Art (commercially speaking) had to be different because it was a Veblen good: an object selling itself by its status as conspicuous consumption–a thing normals could not afford.
But then… due to the quality of printing technology by the mid 20th century, normals could afford reproductions (posters) of almost anything. So the object had to not only display a level of wealth that set the consumer apart but also a level of sophistication. Or, really faux-sophisticaion–that is, an ability to appreciate things normals couldn’t “understand” (i.e. things most people think are boring usually because they are, like the simple and dull objects based on ordinary math formulae that Sol Lewitt produced). This lead to a circumstance where art whose popularity among ordinary people preceded its popularity among the wealthy could not fulfill the requirement of art as an ideological Veblen good: great and popular illustrators had to be considered non-art because if normal people were liking them then the wealthy people who liked them were simply jumping on a taste bandwagon rather than reifying their status as tastemakers. Jack Kirby was worse than Lichtenstein because Kirby reeked of the Street. Lichtenstein’s pitifully minor alterations to Kirby panels were supposedly things only an educated person of fine sensibilities could appreciate. The ordinary person can’t only not afford to own a Sol LeWitt, they can’t even afford to like a Sol LeWitt–it is so boring that a person with no other luxury or solace in their life might kill themselves if they had to look at one. Poor people need art that gives them something–beauty, insight, transcendence. They need it to hold together any sense that life might be worth living. The wealthy can afford to waste their money and time and space in their heads and homes on vapid art: if things get slow they can just climb out of the hot tub and buy something to assfuck and then kill.
This is all the same kind of crisis for the wealthy that’s created when cheap clothing or accessories become popular: how do we stay cooler than everyone else and maintain the idea that we are a protected class for a reason? By pretending our taste is evidence we’re better.
The illustration-vs-art line is basically meant to reinforce this very silly idea: If the street liked it first, it’s worthless.