Possibly the same person:
United States Census, 1870
Citing this Record
"United States Census, 1870," database with images, FamilySearch(https://familysearch.org/ark:/61903/1:1:M8RH-ZJT : 17 October 2014), Ann Alexandine in household of K A Wilbur, South Carolina, United States; citing p. 59, family 489, NARA microfilm publication M593 (Washington D.C.: National Archives and Records Administration, n.d.); FHL microfilm 552,986.
Her son's death certificate lists his father as Alexander Martin:
South Carolina. South Carolina death records. Columbia, SC, USA: South Carolina Department of Archives and History.