I am working on my Master's thesis ( most common). I am working on my Master's thesis project ( can be used and you would be understood, but less common). I don't know that this may also depend on country (?); I work for a University in the U.S., worked on Master's degree and so did both of my parents, but that was many years go.

The "project" is what you actually do. The "thesis" is what you write about it. "For her master's degree project, she spent six months snorkeling and skin-diving, observing the behavior of the bicolor damselfish. In her thesis, she analyzed the behavior and concluded that certain postures were intended to defend territory and others to challenge others' territory."