Closets and Wardrobes

[potioncat]

Carol: 
> I suspect, without looking it up, that the expression "coming out of
> the closet" was originally British, as was "closet drinker." At least,
> it makes more sense to me to have a person (figuratively) hiding in a
> small private room than, say, secretly drinking in a broom closet.

Potioncat:
When I was a child, my family--indeed, the whole neighborhood--attended 
a small, fundamentalist, Hellfire-and-brimstone church. No drinking. 
One day my best friend showed me the liquor her parents thought they 
were hiding in the closet. (built-in wardrobe)

In which sort of closet are skeletons kept?