Vampires don’t like sunlight but moonlight is actually also sunlight
Tell that to the werewolves.
Moonlight is only about 14% reflected sunlight, with a different spectrum (some wavelengths gets more absorbed than others, some more reflected, etc). If the two spectra of moonlight and sunlight were compared side-by-side with no mention of their origin, they basically appear as two completely different light sources, one peaking at the yellow wavelengths and the other peaking at the blue-green wavelengths.
To summarize; moonlight is not sunlight, it is reflected sunlight with a lot of its information lost or altered.
Does this mean that, with the right set-up, you could make light sources which mimicked moonlight accurately enough that it sets off someone’s lycanthropy? I’m not sure what such a device would be useful for, but it’d be neat nonetheless.