I'm not so sure this is the fundamental division.

In my musical pursuits, computer composed classical music, I make the
distinction as

1) popular - music with a continuous drum beat
2) classical - music with no continuous drum beat

I see the continuous drum beat as what distinguishes classical music
(which may have some drums) from popular music which nearly always has a
continuous drum beat - bass, snare, hihat.  (In addition to my interests in
classical music I used to play bass and sometimes drums in a rock n' roll
band.)

The drums, if played properly, pull the song together (we say makes it
tight).  The drums act as a skeleton on which the other parts - rhythm,
bass and lead - are hung.

However, if there is no continuous drum beat, then the form (or structure)
has to take on that role, the fact that passages repeat, motif development,
ornamentation passages, etc., recalling to mind something that was
previously heard.  To me this structure becomes the invisible skeleton that
keeps the piece from being merely a concatenation of music, albeit good
music.

So I would offer this distinction for consideration by the list.  Remember,
there are many ways to divide music into two classes.  I am reminded of the
joke "all people can be divided into two classes - those that divide people
into two classes and those that don't.  But imaging a vocal quartet singing
a piece in sonata form in the 18th century or a modern composition in
sonata form.  To me the vocals are just another voice like the chorus
in Beethoven's 9th.  For me its the continuous drum beat.

Although, one may find, so called popular music without a continuous drum
beat, does anyone know of a "classical" piece with a continuous drum beat
(there may be but I don't know of it)

Bill Pirkle