When someone says that another person "sings a different song," they mean that they have a different opinion or perspective on a particular matter. There are several synonyms that can be used to express the same concept, such as "marches to a different beat," "dances to their own tune," "swims against the tide," "has a different viewpoint," "sees things differently," "avoids the mainstream," "branches out," "takes a different course," "follows a different path," and "has an alternative view." All of these phrases are great ways to express that someone has their own unique way of thinking or doing things.