Bartimeus and Charlestown same tune?

Looking at the tune “Bartimeus (Jenks)” and “Charlestown,” it looks like they are the same melody. As far as we know, this tune was a folk song first published in Pillsbury's The United States Sacred Harmony in 1799. Looking at Warren Steel's Collected works, no such tune name exists in Jenks's repertory (though there are obviously hymnals that have that attribution that should remain as such).