Not a question, even. Distinctions are more along the lines of 'fine' or Popular - equal amounts of craft, talent and skill can go into either.
Popular music is meant to be very direct, immediate communication (most of it songs with texts being as strong a factor as the music itself.) Pop music, regardless of some genres 'more sophisticated' (prog rock, etc.) is still meant to be very straightforward stuff.
'Fine art' includes classical music. This genre can also have simpler and more direct pieces meant to be immediate and more popular, but does require 'more' of the listener, generally, in more intellectual activity to track the musical elements to make any 'sense' of the musical dialogue. A large bulk of the classical repertoire is pure music with no text or literal association, non-illustrative. It is an highly abstract art form.
An analogy would be the difference between a writer making a short story limiting themselves to a more basic vocabulary so the story is immediately accessible to 'the people' (popular / 'pop' comes from the word Latin word "Populi," = "of the people" = 'the masses.')
This is very different from a lengthy novel, with more characters, plot development, and having a much more expanded vocabulary, the author of which is assuming their audience has the expanded vocabulary and is willing to 'work at it' more to sit down and read the entire work.
If you've ever tried to write a short story in limited vocabulary which is still worth reading and has content that moves people, you would never again say it is a 'lesser' task for the writer than composing a larger novel. One does take a greater amount of tools, time and preparation to acquire those tools and skills than the other.
Making really successful works in either genre, works that move people and will continue to move people for more than five years is no mean trick. (The average life-span of pop music, three to five years ~ and, less advertised but fact nonetheless ~ a lot of classical music has bitten the dust within five years of its first production, if not near sudden death right after the premiere.)
Still, in music, it takes a more highly developed vocabulary and much more control of many more structural elements to compose an extended work of twenty minutes duration which is a continued and developed idea, without any exact repetitions, and which will fully hold the interest of the listener. The typical pop song is three, maybe four minutes long, and within that time has as many wholesale repetitions. The fact there are that many more people in the pop arena has two reasonable explanations, the first being in the word itself, People. There are a lot of'em. The next, the basic skill set takes far less time to acquire than the skill set for classical music.
Either way, it is a rare and hardworking talent to come up with something which reaches a lot of people, touches them deeply, and speaks to many people of many generations and for many generations.
There is otherwise no comparing the two, and further comparisons are futile, often making for ridiculous and non-productive arguments.
It seems no matter what terminology you use for each genre, someone will manage to take insult. Classical as Art Music? ... could imply there is no 'art' in popular music, etc.
I'm lobbying - at every opportunity like this one presents - for a more neutral and general set of terms:
POP(ular) and NON-POP(ular).
Best regards.