The former is a commercial song which is (sort of) about the latter, and incorporates its tune; with an additional, modern part added. The traditional tune turns up in other parts of England too, under a number of different names. The "modern" Floral Dance was itself picked up by traditional musicians (in East Anglia, for example), but they usually dropped the "composed" bit. Dates and further details are all given in the earlier discussions here which have already been mentioned.