There have been lots of men named Cornelius Miller.
Your first one is the one interviewed by Chappell and Johnson. His wife was the former Cora L. Wiseman of Ohio, b ca 1868. They married in 1888. In the 1920 census he exaggerated his age, and he did also in 1920 (census) and 1927 (to Johnson). He seems to have died between 1927 and 1930, when Cora is reported in the census as a widow. You note that an LDS record gives his birthdate as 1861. That is correct. The census records for 1910 and 1920, and his self-reported age in 1927, are not correct.
Your second Cornelius Miller is not a son of Andrew Jackson Miller, as is your first one. Chappell reports that his Cornelius Miller is a son of Andrew Jackson Miller.
For some of the details, see