What you're describing is a description of polarization.
As to OAM, it's a bit hard to explain because it's difficult to visualize. Think about an ordinary radio wave going back and forth like a sine wave in a single plane. This is linearly polarized light. Now, with the same frequency and phase another photon could also be polarized at a different angle, say 90 deg. to the other photon. However, you can essentially combine both aspects of waves in varying degrees, creating elliptical and circularly polarized waves. You can think of that as the photon "spinning". OAM is on a different scale. Normally we think of light as traveling in purely straight lines other than the wave effects. However, take that model of a rotating photon wave-packet and at a larger scale imagine the photon "in orbit" along a trajectory, taking a cork-screw path.
Circularly polarized light is like a spinning football being thrown. Light with non-zero OAM is like a curve ball (although admittedly the analogy breaks down).
At first glance, I though OAM sounded like circular polarization with different angular velocities. Now your comment makes me think there's more to it. Maybe someday I'll get back on track for a physics degree, and I'll be able to think through it properly.