The two approaches to use fitLSA function will provide the same results if the inherent data being used is the same. Note that bag-of-words and count matrix are just ways to represent the input data so that it can be interpreted by the algorithm. Two different approaches provide flexibility for the user trying to work with this function.
In this case, bag-of-words and count matrix both give the count of the words in the documents but in different formats. One uses a bagOfWords object, whereas the other uses a matrix of nonnegative integers to represent this information.
