Wet and Dry lube are pretty much universal terms, they're not constrained to one manufacturer.
Wet lube is suitable for wet conditions, dry lube is suitable for dry conditions.
Wet lube is quite sticky. It will stick to your mech and is less likely to get washed off by rain. The downside, because it is sticky, it can pick up crap from the road, as those guys said.
Dry lube is a much lighter lube. It should keep your mech quite clean, the downside is that because it is that much lighter, it'll get washed off in wet conditions.
As regards use, it really depends on where you live and your climate. Where I am (UK) I tend to use dry lube in the summer and wet lube in the winter. If I think I can get away with it, I'll lean toward dry lube (although I won't put dry lube on top of wet lube, I'm more likely to clean the chain first).
Incidentally if you look at a given manufacturer, they will likely have both wet and dry products, possibly others too. All are optimised for certain conditions. For example, the manufacturer White Lightning makes four lubes (described here). I use Epic (which is a dry-ish lube) and Wet.