Minor Cleveland Adams, born 9 March 1892, Lancaster Co, SC, registered for the WW1 draft on 5 Sep 1917 as a resident of Williamston, Anderson, SC. He was working as a "textile operative" at Williamston Mills. He was married. He had lost an eye, and at the time had a fever. He was described as tall, medium build, grey eyes, and dark hair. He signed his name with an "X".
The 1910 census has Jim as 50 and Sarah as 55 You probably are right about the 1910 census in Greenville showing the same folks as the 1900 in Lancaster.
The 1900 census has Cleveland born March 1889, age 11. The 1910 showed him in Greenville as 17, that at least roughly fits with the 1892 birth date.
The 1910 entry shows Jim as 50 and Sarah as 55. In 1910, Sarah was the mother of 5 living children out of 6. Possibly Burrell was deceased. Thomas 18 in 1900 could be Tom 22 in 1910. Annie 15 in 1900 has no counterpart in 1910. Married off? Stephen 13 in 1900 could be Steven 19 in 1910. Cleveland 11 in 1900 could be the garbled named starting with Cle... age 17 in 1910 Mattie 8 in 1900 could be the Mattie 16 of 1910. In 1910 there was a daughter-in-law, Ruby, 17.
There was another 1910 listing of a Stepens Adams 22 SC and Ruby 18 NC at Williamston, Anderson, South Carolina, married one year. Both worked at a cotton mill. Double count?
There is a WW1 draft registration for one James Steven Franklin Adams, born 12 Jan 1888 in SC. Wife Ruby. Farmer. Described as medium hight and build, brown eyes, black hair. Reident of Iva, Anderson Co, SC [aboyt 25 miles from Williamston].