Lets take these three games for example: Street Fighter, Tekken, and Blazblue.
Now lets start with simple notation. Street Fighter has 6 buttons where as Tekken and Blazblue are mostly 4 button fighters. Jab Strong Fierce (LP,MP,HP) and Short Forward Roundhouse (LK,MK,HK) in Street Fighter versus 1 / 2 (Left punch/Right punch), 3 / 4 (Left kick/Right kick). Tekken and A,B,C,D in Blazblue. The directions in Street Fighter and Tekken are interchangable where as in Blazblue directions are annotated by numbers:. Special characters like, (+) is common for simaltaneous, but (~) is used in Tekken is means rapid succession. Then even more complex game mechanics are notated differently in games like RC (Rapid canel) (BB), FADC (Foucs attack dash cacnel) (SF), and WS (While standing) (T). Confused yet? This is just concerning simple notation. Not to mention that Tekken is a 3D game where you have to account for an additional axis.
You see other factors like timing for combos, spacial recognition, muscle memory, system engine and combo mechanics are different in other fighting games. Street Fighter being the most consistent of the fighting game tree.
CLASSIC Layout its almost timeless...
Players often engrave these aspects into their minds transitioning from one fighting game to the other is very tasking and in many cases difficult. A fighting game player doesn't have to start from scratch for every new game they play, however the learning curve for a completely new player can be considerably less steep because there is nothing to re-learn. Take this funny, yet relevant, video comparing Rosetta stone and Fighting games hosted by the creative minds at Screwattack.
Which is why a person that places well in tournaments across the board is a rare quality. Tokido would be the best example of this. Evolution 2K11 where he makes it to top 8 in BBCS2, Tekken 6, and Super Street Fighter 4. In contrast Ryry, a competitive player from the east coast, plays multiple fighting games but doesn't place as well as Tokido. Of course this is a topic for another time when we jump out of the small realm of notation and linguistics and the much deeper psychological realm of Playing to WIN vs Playing for perfection.