What the hell is a "C" rating?
The C rating is an imaginary figure that they started putting on LiPo batteries to figure out the amount of amps it can safely handle. In theory all batteries have a C rating but they don't tell you what it is for NiCd or NiMh batteries but its generally 10c or lower which is why you need a 3300 or 3600mHa battery to get better performance from your airsoft gun. Lipo batteries have a much higher C rating in a smaller package and can handle more amps than the other two.
Usually, thats called the "amperage rating", and is represented by IC, or "Amperage Capacity". There are a lot of different things that C could be from your description, either Amperage Capacity, which means the maximum current in amps that the battery can sustain before taking physical damage, or nominal capacity (normally IsubN), of which the product in question is the current that it should be delivering/capable of handling during normal operating procedures.
Just wanted to clarify, there are big difference between those two above, which from the description you gave, "C" could mean. C isn't used in any standard I use. Doesn't mean it doesn't exist, since product producers don't need to use a standard. Also, a battery is read in discharge rate, not how much the battery can handle. I assume thats what C means, its discharge rate (ideal for airsoft, from my experience, is around 25A discharge rate, or 25C according to the symbol you brought up).
Again, I am also looking at this from a different field of power, so, well, anything goes with the amount of symbols out there in power engineering alone...