What's the difference between a piano cover and a just a piece?

Question

This is completely random, and I just see everywhere piano covers, and others piano pieces.

Answer 1

A piece is generally an instrumental work of music, commonly used to describe classical music.

I have never heard anybody use the term "piano cover," but I suspect that it would mean the same thing as playing a musical arrangement of a modern song, or simply performing covers of new age piano artists.

Usually, the word "cover" is used when an artist performs or records another artist's song and stays close to the original, including similar instrumentation.  

Answer 2

I don't know really how this relates to piano arrangements, but a "cover" of a song means that the performers are not performing their own work but are covering (playing) a song made famous by another artist.  For example, Smashmouth did a "cover" of the Monkees' song, "I'm a Believer"

How this relates to your question I'm not quite sure except to say that it might mean a piano cover is a remake or an original music piece with maybe slight variations in the arrangment; whereas a simple piano piece is an original arrangment of music.

Does this make sense in the context of your question?  Hope so.