Hey @barton26,
I don't think so, it seems to be the very same system! I tried to find out since when the Milpa is grown, but could only find that has been part by the Mayan culture for several centuries. I also noticed therefore that it is not South, but Central America where it came from (geography, ahem... ;) ) and updated this in the post. I think there was some exchange between the Mayas and the Native Americans, and especially effective agriculture can spread rather quickly. I can not tell you at this point who copied whom, but I will try to find out!
Glad I could help correct the post! It does make sense that the knowledge of these crop growing techniques could have easily spread across the Americas. Thank you for the knowledge :)