Patrick Nielsen Hayden sends us to the Turnip Disambiguation Page of Wikipedia:
Scientific term Brassica rapa rapa Brassica napus or B. napobrassica Pachyrhizus Southern England, most Commonwealth countries turnip swede (= Swedish turnip) yam bean United States turnip rutabaga or yellow turnip jicama Ireland and Northern England turnip swede Scotland swede, tumshie or white turnip turnip or neep Cornwall white turnip turnip Malaysia, Singapore, and Philippines turnip Atlantic Canada turnip jicama also called white turnip or summer turnip yellow turnip or winter turnip sweet turnip
Brassica napus and B. napobrassica are called swedes (a shortening of Swedish turnip) in England, especially in the South, and in most dialects of the Commonwealth. Rutabaga is mostly an American word. The rutabaga or swede differs from the turnip (Brassica rapa) in that it is typically larger and yellow-orange rather than white.
However, in some dialects of British English the two vegetables have overlapping or reversed names. In the north of England and Scotland, the larger, yellow rutabagas are called neeps (from an Old Norse term, not a shortening of "turnips"), or turnips from folk etymology, while the smaller white turnips are called swedes.