What we mean by the spin of a particle is the subgroup of the Lorentz group that commutes with its 4-momentum (the "little group"). For a particle with mass, go to its rest frame where the 4-momentum is Pμ = (0,0,0,1) and the spin operators are the rotations in 3-space, Sx, Sy and Sz. They form SO(3).
For a massless particle there is no rest frame, so take the 4-momentum in the z-direction, kμ = (0,0,1,1), and its spin operators are the three operators that preserve kμ.
The first one is a rotation in the (x,y) plane. This is the helicity. It acts on the components of the particle's 4-potential as Ax ± iAy → ±(Ax ± iAy).
The other two are null rotations, x → x + εk and y → y + εk. These operations just add a multiple of k to the 4-potential. But this is just a gauge transformation. So helicity is the only observable part.