The mass of a helium nucleus is less than the mass of two isolated protons and two isolated neutrons. When the component hadrons are assembled, this mass is lost as energy ($E=mc^2$). This makes it (at least sort of) seem like mass is a kind of potential energy. Matter and antimatter can annihilate each other, releasing energy ($E=mc^2$). This also makes it (at least sort of) seem like mass is a kind of potential energy.
If I have a mass at approximately sea-level on Earth, will flying it away from Earth increase its mass? (If so, is this related to relativistic mass?)
The original question doesn't really ask what I mean to ask. Suppose that, after the mass has been flown into space, it is stopped relative to Earth. (I think that would require a geosynchronous orbit.) Would its mass be different than it was before it left Earth?