> I think I heard somewhere that the speed of light changes when it passes through different
> medium, thus explaining the diffraction of water. Did I get that mixed up somehow?

Yes. That's the explanation for refraction. The light slows down as it enters the water (because
it's denser than air) and speeds up again as it leaves. Result: Things that are partly in the
water look like they bend at the surface.

Diffraction is the one where light spreads out after passing through a narrow slit.

> I also heard that the number we use for C is only referring to the speed of light in a vacuum,
> and that different mediums have different speeds of light. Or is it that the light slows down when
> transitioning between mediums?

Light slows down when moving into a denser medium (from air to glass, say) and speeds up
when moving into a less dense medium (say from glass to air).

c is the speed of light in vacuum, which is assumed to be the fastest light can travel,
because there isn't any medium less dense than vacuum.

> Or is all of the above irrelevant because the "refractive index" has nothing to do with the
> speed of light?

Refractive index is the ratio between the densities of the two media, and thus relates to
the proportion by which the light changes speed when passing between them.