Einstein's famous E=mc² equation is actually a special case of the general equation [1]
E²= (mc²)² + (pc)²
Where m is the rest mass of the particle (the mass measured when the particle is stationary relative to the observer) and p is the momentum of the particle.
Therefore when we discuss high-energy particles, we mean they have high-energy associated with their high momentum (velocity).
Typically the comsic rays are near-light speed protons. Although they maybe light nuclei.
[1] https://physics.stackexchange.com/questions/143652/is-e2-mc2...