I found another bit of information to support the belief that Benjamin Simonds who was born at Nottingham West, NH, 16 November 1761 (son of Daniel and Martha Simonds) is the same as Benjamin Simonds of Amherst and Antrim, NH.
Benjamin Simonds of Nottingham West had a brother Joseph Simonds who was also born at Nottingham West, NH 19 September 1757. According to his Revolutionary War pension records (W2673, Bounty Land Warrant #33765-160-55), he lived in that part of Amherst, NH that later became Mont Vernon, NH and enlisted from there as a soldier in the Revolutionary War. Benjamin Simonds of Amherst and Antrim also lived in Mont Vernon before 1793, and perhaps moved there with his brother Joseph before the Revolution.
Joseph Simonds then moved after the Revolutionary War to Wilton, NH where he lived for 40 years before moving to Brookline, MA and then to Truro, MA where he applied for a pension 17 August 1832. He died, apparently in Truro MA, 8 April 1836. He married Bethia Spaulding at Townshend, MA, 20 December 1821 (don't know if this was his first marriage or not).