Halloween, Oct.31st, is of course the eve of All Saints Day, Nov 1st. All Souls Day was Nov 2nd, but the souling songs and plays were often performed on All Souls Eve, or the evening of Nov 1st. To further confuse matters many of the songs and customs predate christianity anyway and are more to do with Samhain, the pagan festival which took place around the beginning of November.
According to Brewer it is coincidental that the Catholic church holds All Souls day so close to Halloween, Click here
here is an interesting article about souling.