This is my understanding as well. All massless particles must travel at the speed of light (they cannot be slowed down) and moreover, they must travel at the speed of light in all reference frames.
Whereas massive particles can remain at rest. There's no such thing as an unmoving photon.
My point is subtly different, I think. The point I’m trying to make is that if you’re “at rest” in space, all of your movement is through time. If you are “at rest” in time, all of your movement is through space.
As far as I understand it, having mass is basically a result of moving more slowly through space.
Whereas massive particles can remain at rest. There's no such thing as an unmoving photon.