In "The History of Portland, Maine" by William Willis Published by The Maine Historical Society on pg 300 it says
" Wallis. Persons bearing this name in Falmouth were numerous during the second settlement. The first of the name were Nathaniel and John, who were probably the ancestors of all the rest; they were both here before the first war. Nathaniel lived at Back Cove, and John on Pupooduck Point; In addition to these were Josiah,b. 1662, and was living in Gloucester 1734, Benjamin, Joseph, and James, who was b. 1670 and lived in Purpooduck; these were all sons of John; the went to Gloucester after the destuction of the town, but returned again.Josiah's son Johnwas an inhabitant of Cape Elizabeth in 1768. ( there are a few sentences I am not including...however Nathaniel b. 1632 was living in Beverly 1701 and had a son John whose son John was living in Sherburn, Ma in 1790."Hopefully this clears up confusion about John and Nathaniel Wallis. ( a note of the pg bottom states they were both b. in Cornwell, England.