We present a simple approach for deriving velocity-dependent masses using the principle of relativity. Our analysis reveals that the transformations associated with Galilean, Lorentz, and other space-time frameworks between two inertial reference frames are fundamentally equivalent in the context of the relativity of mass. Consequently, the notion of velocity-dependent mass is not the exclusive characteristic of Special Relativity (Lorentz transformation). Among the notable conclusions drawn from our formalism are: mass can both increase and decrease with velocity, a particle can never be completely at rest, and superluminal signaling is in principle feasible. Furthermore, we discuss on the nature of mass and argue that a photon is not massless.