The staghorns have one of the smallest if not the smallest number of varieties in the plant kingdom. There are less than 20. I have five varieties. You will almost surely have the Platycerium bifurcatum, since it is the common one. You might have the sub-variety of bifurcatum, the 'Neatherlands' but they look the same. The 'Neatherlands' wll take more temperature extremes and will handle dryness a bit better than the standard bifucatum. The other varieties are very rare and can be very expensive. The care is basically the same until you get into the really rare varieties. Those are seldom if ever seen for sell.
You probably are referring to sphagnum moss.
These are a pair of two-year old staghorns mounted on cork. The older they get, the more pronounced the forks in the fronds will be, thus their name "Staghorn". The fronds of these pair of young plants have not developed that deep forking yet. The light green, oval growth is called the basal frond and the elongated "leaves" are called the vegetative or spore fronds. Some people call these plants "Elkhorn Ferns", but the elkhorn is not even in the same family as the staghorn.
