What is the difference between the way light travels in a gravitational field and the way it travels through an expanding universe? A photon is travelling through space. As it travels, the space through which it travels is expanding

Does this describe


A - a photon travelling from a distant galaxy to earth
B - a photon travelling from a point of higher to a point of lower
gravity
C - either


If like me you think the answer is C, can you explain why light should travel differently through a gravitational field to how it travels through an expanding universe? In other words, why in one case does the speed of the photon vary, while in the other case it doesn't? 

Alternatively can you explain why you don't think it's C?

I have asked a similar question on the Physics Stack, but I probably worded it badly, so I just got a load of down votes and no answers. I hope I haven't offended anyone here with this wording.
If like me you think the answer is C, can you explain why light should travel differently through a gravitational field to how it travels through an expanding universe? In other words, why in one case does the speed of the photon vary, while in the other case it doesn't?


I think the reason is, we can take the Cosmological redshift as a Doppler redshift, where the speed of the photon does not change but only the wavelength changes due to the expansion of the universe.

Meanwhile, in Gravitational redshift, its the "redshift" is purely caused by GR and it's possible that the light loses its speed due to this effect.

Here is the link why I think cosmological redshift can be thought as Doppler redshift. 

Here