A windsurf store is generally going to be a local surf shop that’s all grown up. Windsurfing has a much larger set of equipment that it uses every time you go out, from a harness and rigging, to the mast and sail, and as such a surf shop generally has to be pretty well established before it can afford to stock windsurfing equipment.
That is not to say that you can’t find a perfectly good windsurf store that opened its doors as such, it is just much less common than seeing one as an expansion opportunity for an established surf shop. Windsurfing is a more extreme version of surfing, and in addition to the equipment needed to do it, there is also a full set of safety equipment that you should be using as well.
A windsurf store will be able to sell you a well fitting board harness, but those are just the beginning of what you’ll want to keep yourself safe. You will also want to pick up a helmet that fits securely, because it won’t do much good if it comes off as soon as you tip your head sideways. As a matter of comfort, if not life and death, you will also want a wetsuit. These handy suits will help keep your body heat as you are knifing through the wind.