What are dB(A) and dB(C)?
The human ear doesn't hear all sounds at the same level and your ear amplifies a specific part of the frequency range meaning you hear it more loudly than other sounds. That change can be quite dramatic and can by up to about 28dB at the 4 to 6kHz range. If we therefore just measure the flat number of decibels of the noise we won't be taking account of the extra volume your ear gives to certain frequencies, and as it is volume which causes damage this is a problem.
So we use dB(A) which is called the A weighting. A weighting means some mathematical jiggery pokery is done by the meter to mimic the way a human ear works and gives you a result which is the same as someone would hear it after their ear had amplifies parts of the sound. A weighting is used for the main 85dB(A) limit.
A weighting also has a time element in it, with the result being averaged over time, which could be the duration of the measurement or the length of a full shift, or anything between. C weighting - dB(C) - has no time element and is used for short-duration impact noises. Essentially very short peaks, and is what relates to the 137dB(C) exposure limit.
The best example I can think of off the top of my head is a factory with a machine that is shrink-wrapping pallets. As the machine runs we would measure its noise in dB(A) and that's over a period of time. Once the pallet is full it is taken away and someone drags a new pallet over and then just drops it into place. That half-second bang as it hits the floor is what we measure in dB(C).
It's worth highlighting that dB(C) levels are almost always much higher than dB(A) measurements so don't be surprised to see something which is say 79 dB(A) and 112 dB(C). That would be perfectly fine and is well below the noise exposure limits.