I wonder what would be the main difference between arpeggiated accompaniment and counter melody.

Could it be the rule that an arpeggiated accompaniment would be more repetitive (because it consists mainly of chord notes), whereas a counter melody would vary more in terms of notes used (without sticking to chord notes only and repeating itself as frequently as it would in the accompaniment).

The song I'm going to refer to:

In this song, I believe that the piano is playing arpeggiated chords accompanying the voice of the singer. Counter melody would be, I assume, when the piano was doing entirely its own thing without as much repetition. What are your thoughts about it?