They're pretty much the same, although 'liquor' is more colloquial. As far as I can recall, I've only seen 'spirits' used in articles from food/beverage magazines, blogs, store signs, etc.
I probably wouldn't ask for the best liquor or spirit in a store, though. I'd probably specifically ask what their best vodka/gin/bourbon/wine/whatever was, depending on what I was looking for.
Note that 'liquor' excludes beer and wine, however. 'Spirits' could be any alcoholic beverage.
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