Flare vs veiling glare

[Bill_1856]

What is the difference?

[Jack Dahlgren]

They both have the same cause - internal reflections.
I'd define flare as distinct areas of brightness and veiling glare (your term, not mine) as a general loss in contrast across most of the image.

[Dan Fromm]

We are poor little photons who have gone astray,
baa baa baa.