I think it's simply that the eyes momentarily open a little wider, which thus makes them briefly stand out, as they're more reflective than skin. You'll also see descriptions of "eyes bright with fear" etc.

You can also have faces lighting up, but that's more obviously metaphorical, presumably driven by the upward "lift" of facial muscles in a smile.

As for the latter sentence, I think what happens there is that they use "face" to mean the muscles of the lower face (below the cheekbones) and "eyes" to mean the muscles of the upper face. A lot of emotion is conveyed in the upper face and periocular region rather than the lower face. So much so, in fact, that the nerve supply of the two regions is quite different.