There is rest mass, which is the mass of an entity when it does not move. And there is relativistic mass, which is the rest mass plus the mass due to all of the kinetic energy of the entity. Photons have zero rest mass, but depending on the energy they carry, they have different relativistic masses.

By the way, only entities with zero rest mass can move at the speed of light. Actually, in relativity it is mathematically inconsistent for something with zero rest mass to exist unless it is moving at the speed of light.