# Spatial variation in velocity of light or curved space-time?

In the case of spherical symmetry you can say that the velocity of light (in coordinate time) goes as:

$$v_{light}=c(1-\frac{2GM}{rc^2})$$

in the radial direction and as:

$$v_{light}=c\sqrt{(1-\frac{2GM}{rc^2})}$$

Some instead tend to say that the velocity of light is always the same but "space-time is curved" in a certain way.

Are these equivalent ways of saying the same thing?

Question: Are the statement that "there is spatial variation in the velocity of light in a spherically symmetric gravitational field" and the statement that "the velocity of light is constant but spacetime in a spherically symmetric gravitational field is curved" equivalent statements?