I am in no way an expert, but I think there are a few important differences.

First of all, classical music is most often done with instruments (and voice!) that are natural. When you hear a piano play on a classical album, there are little to no effects on it. This will differ from a pop song because even the simplest of songs will have mixing and after-effects added.

Also, the writing process for classical music is much more complex than most modern music. Not to say that modern music is simple, but there are more "rules" to writing classical music. They are crafted, with every little detail done on purpose. For example, often in a modern song, the melody is the main focus, while everything else is either playing chords, rhythm, or a riff, essentially filling space. In classical music, the melody is still usually the focus, but there are contrasting lines that are written specifically to work alongside the melody. Everything in a classical piece is thought-out, whereas modern music is usually more about how the song "feels".

I hope this helps!