The word turpentine orignally meant sap from certain conniferous trees (nowadays we refer to these saps as balsams). So Venice turpentine, for example, is a thick, sticky sap from larch trees. If you distill a turpentine, you get a thin substance that makes an excellent solvent: spirits of turpentine. Over time, as real turpentines fell into disuse and spirits of turpentine became a common household item, people started using the word "turpentine" incorrectly to refer to the solvent, not the sap.
That's confusing when you are trying to talk about artist's materials, however, because balsams such as Venice turpentine, Strasbourg turpentine, and Canada balsam are still in use. And, of course, spirits of turpentine are commonly used to thin paint. I try to use "spirits of turpentine" or "turps" to refer to the solvent.
Venice turpentine, by the way, isn't named after the city. It's a corruption of "vernice turpentine." "Vernice" is an old way of spelling "varnish." So Venice turpentine is a balsam that was commonly used in varnishes.
The Venice turpentine you can get in art stores is very expensive. It's also used in the care of horse's hooves, and you can get it much more cheaply from a tack shop.
Aren't I full of marginally useful information?