  Strong magnetically dominated Alfv\'enic turbulence is an efficient engine of
non-thermal particle acceleration in a relativistic collisionless plasma. We
argue that in the limit of strong magnetization, the type of energy
distribution attained by accelerated particles depends on the relative
strengths of turbulent fluctuations $\delta B_0$ and the guide field $B_0$. If
$\delta B_0\ll B_0$, the particle magnetic moments are conserved and the
acceleration is provided by magnetic curvature drifts. Curvature acceleration
energizes particles in the direction parallel to the magnetic field lines,
resulting in log-normal tails of particle energy distribution functions.
Conversely, if $\delta B_0 \gtrsim B_0$, interactions of energetic particles
with intense turbulent structures can scatter particles, creating a population
with large pitch angles. In this case, magnetic mirror effects become
important, and turbulent acceleration leads to power-law tails of the energy
distribution functions.
