rest mass vs total energy
Think of a wound-up spring versus a spring that is also being thrown across the room. The wound-up spring stores energy just by being what it is; the thrown spring has that stored energy plus the energy of its flight. A particle is similar. Its rest mass is the energy permanently locked inside it — the energy it would have even if it sat perfectly still. Its total energy is that plus the extra energy it carries because it is moving.
Rest mass (often just 'mass') is an intrinsic, unchanging label: an electron's is about 0.511 MeV worth of energy, a proton's about 938 MeV, and that never changes no matter how the particle moves. Total energy, by contrast, grows without bound as the particle speeds up — it equals the Lorentz factor gamma times the rest energy. The difference between total energy and rest energy is the kinetic energy, the pure energy of motion. At the LHC a proton's rest energy of 938 MeV is dwarfed by its total energy of 7 million MeV; almost all of it is kinetic.
Keeping these straight prevents real confusion. Modern physics treats rest mass as the fixed, invariant quantity and reserves the word 'mass' for it; the older idea of a velocity-dependent 'relativistic mass' that grows with speed has been largely abandoned because it muddles the bookkeeping. What actually grows with speed is total energy and momentum, not mass. So a fast particle is not 'heavier'; it simply carries more energy. The rest mass is the particle's true identity card, the same in every laboratory and every frame.
total energy = gamma x rest energy; kinetic energy = (gamma - 1) x rest energy. A 7 TeV LHC proton has gamma about 7,500, so its kinetic energy is roughly 7,500 times its 938 MeV rest energy.
Rest energy is fixed; total energy and kinetic energy climb with speed without limit.
Avoid the obsolete phrase 'relativistic mass': mass means rest mass and does not change with speed. Saying a fast particle is heavier is a misconception; it carries more energy and momentum, not more mass.