I think you are talking about three different Samuel Adams.
(1) Samuel Adams (1781-1843) was born in Putnam County NY, moved to Delaware Co. OH about 1830 and died there. He married twice: Catharine Nichols (1781-1834) and Martha (---) Ridgeway (1796-1888). He was designated as Samuel Adams II in the 1840 census.
(2) Samuel Adams (1770-1844) married Rachel ---(1776-1823) was born Waterbury CT, moved to Delaware Co. OH about 1805 and died there. Two of his grandchildren married into the Putnam Co. NY Adams family.
(3) Samuel Adams (1781-1860) was born in that part of Albany Co., now Greene Co. NY. He moved to Olive, Ulster Co. about 1839 and died there. He married Hannah Gilbert (1779-1866) who was born in Dutchess Co. The earliest deed I have on him is 1802 for Samuel Adams of Catskill when he bought land from John Darby. This Samuel Adams MAY be related to the Putnam Adams family. His father was POSSIBLY William Adams of Coxsackie.