In general, up until eight maids a-milking they are the same no matter which version you sing (although sometimes the four calling birds are mockingbirds instead, or even colly birds - an Old English name for blackbirds) but after that, it seems anything goes.
It seems that the gifts of the last four days can appear in pretty much any order. Instead of nine ladies dancing, ten lords a-leaping, eleven pipers piping and twelve drummers drumming you could have nine drummers drumming, ten pipers piping, eleven ladies, or even dames, a-dancing, and the twelve lords a-leaping. There is even one variation in which ten fiddlers fiddle, so doing the pipers out of a job. (Of course What is Myrrh Anyway? goes into this in much greater detail.)
And then there are the alternative versions of 'The Twelve Days of Christmas'. One of my favourites has to be the Australian version.
On the twelfth day of Christmas, my true love sent to me