You may have just one man here. The census takers recorded what they heard, therefor the spelling of names is rather suspect. If all the other facts indicate it is one family, I would not worry that the spelling does not match.
Here is a death record of a man born in Louisiana who may be your man. Unfortunately, his mother's maiden name is not included.
"Illinois Deaths and Stillbirths, 1916-1947," database, FamilySearch(https://familysearch.org/ark:/61903/1:1:N3C4-GLL : 27 December 2014), Patrick Prescott in entry for Patrick B. Prescott, 06 Mar 1931; Public Board of Health, Archives, Springfield; FHL microfilm 1,892,956.
And the marriage record, which you have seen:
"Louisiana, Parish Marriages, 1837-1957," database with images, FamilySearch(https://familysearch.org/ark:/61903/1:1:QKJH-5VGV : 15 October 2015), Patrick Prescott in entry for Patrick Prescott and Josephine Baumann, 08 Jun 1898; citing Orleans, Louisiana, United States, various parish courthouses, Louisiana; FHL microfilm 912,049.
This seems like the family in the 1870 census Louisiana:
"United States Census, 1870," database with images, FamilySearch(https://familysearch.org/ark:/61903/1:1:M87K-HBS : 17 October 2014), Patrick Prescott, Louisiana, United States; citing p. 171, family 1636, NARA microfilm publication M593 (Washington D.C.: National Archives and Records Administration, n.d.); FHL microfilm 552,029.
Hope this helps! -NGP