No real difference. They're just old-fashioned terms that don't really mean anything anymore. (Like "dungarees" and "blue jeans" means the same thing.)
Japanese Water Stones (which are rare and very expensive) require you to use water.
I recommend you use all others dry. The oil they recommend is mainly to maintain the stone and only hinders sharpening.
If you find something you're interested in, post here and you'll sure to get a lot of opinions.
As far as regular ole' flat "bench" stones go, I recommend Norton Stones.
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