Spelling was not consistent back then. For Samuel, founder of Hartsel in Park County, it is spelled Hartsell in the 1870 census, and Hartsel in the 1880, 1900, and 1910 census. His father is Hartzel in 1830, Hartsall in 1850 and Hartzel in 1860. His brother George is Hartzell in the 1860 and 1870 census, Hartsill in 1880 and Hartsell in 1900. Brothers William and Joseph are Hartsel in the 1880 Park County census. William is Hartsel in 1900 but Joseph is Hartsell. When searching, I usually try Har* so I get all variations.
I do not think Frank Hartsel is an immediate member of the Jacob Hartsel and Catherine Hartman family.