If I understand, you want to discriminate between different guns by the sound of the shot to determine which one fired. I assume you have done a web search and come up empty.
I would start by learning about FFT - Fast Fourier Transform, which will break the signal down into it's frequency spectra. Alternatively you could make several bandpass filters with different frequencies. Either of these will give you data like you would see on an audio equalizer. From that you should be able to test different guns and see what the spectrum look like.
The math involved in FFT may be too much for an Arduino in real time, but I don't know. I've never done FFTs, only used the results.
If you just want to determine when a shot occurred (not tell which gun fired) then a simple comparator can be used. There will be a big spike in the signal at the moment the gun fires.