We use 3D fully kinetic simulations to study different turbulence modes and turbulence anisotropy of relativistic turbulence in magnetically dominated collisionless plasmas. We extend the method developed by J. Cho & A. Lazarian for decomposing nonrelativistic magnetohydrodynamic (MHD) turbulence into Alfvén, fast, and slow modes to the regime of collisionless plasmas. We find that Alfvén and slow modes are anisotropic, following the P. Goldreich & H. Sridhar scaling, while fast modes are isotropic. We observe a larger kinetic energy fraction of fast modes compared to that found in the nonrelativistic MHD turbulence, suggesting a stronger coupling of Alfvén and fast modes in relativistic magnetized turbulence in collisionless plasmas. We further examine the dynamic alignment and find a weaker scale dependence of the alignment angle than previously proposed. The dominant thermal fluctuations in the kinetic range can cause flattening of the turbulent velocity structure function and weakening of the turbulence anisotropy and dynamic alignment near the kinetic scales.