A wood witch is one perfect for keeping you warm ... when you chuck 'em on a fire to burn of an evening
Honestly that site listing "Sea or Water Witch, or a Hedgewitch and a Kitchenwitch. (To name just a few.) There are Celtic tradition Witches, Saxon Witches"
Generally I would take the name to mean a witch of the woods, one who feels most comfortable or connected there. But a witch shouldn't be defined from any one area since a witchs entire life should be effective all over. A kitchen witch is happiest in her kitchen brewing and making food stuffs, a garden witch happiest in her garden, a water witch happiest when drowning ...

Sorry, it's just too much all the 'I don't think I fit because I can't be arsed to research properly so I'll make up what I think I am' witches. Witch pure and simple whatever you're happiest doing. Otherwise we'd have sex witches, no hang on, that's been done too