If there is original song and same song performed by another artist, when to use term 'remix', 'cover', 'tribute to'?
What you are looking for a is a cover, an existing song performed by a new artist, that is, not the original artist.
A remix is a mixture of some sounds from the original with other sounds. A common example is a pop song to which a beat is added.
A tribute is simply a song that is created or performed in honour of someone or something else, for example a new song written in a style similar to another song.