Summing audio is the most commonly known method of combining audio streams, similar to what any audio mixer does.
Technically, summing audio is simply what it says it is: it adds the value of the samples across all the streams into a new value. Usually there is a gain change (a multiplication) before the samples are summed, because the resulting value can easily go over the headroom of the resulting audio stream.
The "average" of a group of audio streams is the sum of the value of the samples divided by the number of streams.
As compared to summing, this has a sort of "auto-gain" effect by insuring that if the original samples are within -1.0 -> +1.0 that the final output will also be within the same range because of the division involved.
The "difference" of a group of audio streams is the addition/subtraction of groups of 2 streams at a time:
Odd-numbered streams are ADDED to the result stream
Even-numbered streams are SUBTRACTED from the result stream
This is generally only used in stereo streams where the value of the samples in the second stream are subtracted from the first stream. However, we had to extrapolate the rules to be able to handle more than 2 streams, so this is what we came up with - there is no standard and there are no rules for the "difference" of more than 2 streams at once.
The "average difference" of a group of audio streams is the same as the "difference" of the streams, but then divided again by the number of streams.
This combines the "difference" result with the "auto-gain" feature of the "average" method.