This. The quantity that “truly” exists is the energy-momentum 4-vector P. A vector exists independently of any particular reference frame. Its components, on the other hand, depend on such a reference frame.
Seen from a given reference frame, the temporal component of P is the energy E, its spatial components are the momentum 3-vector p, and its magnitude is the rest mass |P| = sqrt(E^2 - p^2) = m. The minus sign rather than plus sign is due to the Lorentzian signature. It is very helpful to visualize these quantities geometrically as 4-vectors in 4-dimensional space.
Seen from a given reference frame, the temporal component of P is the energy E, its spatial components are the momentum 3-vector p, and its magnitude is the rest mass |P| = sqrt(E^2 - p^2) = m. The minus sign rather than plus sign is due to the Lorentzian signature. It is very helpful to visualize these quantities geometrically as 4-vectors in 4-dimensional space.