It appears that
async.waterfall allows each function to pass its results on to the next function, while
async.series passes all results to the final callback. At a higher level,
async.waterfall would be for a data pipeline ("given 2, multiply it by 3, add 2, and divide by 17"), while
async.series would be for discrete tasks that must be performed in order, but are otherwise separate.
Both functions pass the return value, of every function to the next, then when done will call the main callback, passing its error, if an error happens.
The difference is that
async.series(), once the series have finished, will pass all the results to the main callback.
async.waterfall() will pass to the main callback only the result of the last function called.