They're the same value, but light is irrelevant in the matter. PBS did a pretty nice presentation on the subject:
Yep, those PBS SpaceTime videos are excellent, and that one is especially good. Photons are massless, and would travel infinitely fast if not for the universal speed limit. As it is, because photons travel at c, they are timeless from our point of view, meaning they can't undergo change, meaning they never decay. That's why photons emitted at the beginning of the universe can still be reaching us after having traveled 13.8 billion years through space.
So . . . photons are disconnected from the Higgs field? And yet can still be influenced by gravity. Hmm . . .
IIRC, gravity interacts with energy-momentum, not mass (E=MC^2 links mass to energy-momentum). So a particle needn't be associated with a Higgs field for gravity to exert an influence on it. That's pretty much the remote edge of my physics-fu though...
