Elsie B shows in the 1900 census, but has no birth record. Nelly has a birth record. They both were born January 1888. It is probable that they are the same person.
Sources
"Wisconsin Births and Christenings, 1826-1926," database, FamilySearch (https://familysearch.org/pal:/MM9.1.1/XRY2-8XT : 11 February 2018), Nelly Archibald, 13 Jan 1888; citing Waukesha, Wisconsin, reference p 11; FHL microfilm 1,305,602.
"United States Census, 1900," database with images, FamilySearch (https://familysearch.org/pal:/MM9.1.1/MM2G-C3X : accessed 7 March 2018), Elsie B Archibald in household of Gilbert Archibald, Waukesha city Ward 3-4, Waukesha, Wisconsin, United States; citing enumeration district (ED) 142, sheet 5A, family 93, NARA microfilm publication T623 (Washington, D.C.: National Archives and Records Administration, 1972.); FHL microfilm 1,241,822.