I can't tell you how many Connecticut residents make this mistake, even after living here for years. East Hampton has to be east of Hampton, right? Actually, the opposite is true. East Hampton is west of Hampton. They're about a 45 minute drive apart, in two different counties, and two very different towns.
According to the Chatham Historical Society, East Hampton started as East Middletown, became part of Chatham, and separated to form East Hampton in 1915. Known locally as "Belltown," East Hampton had strong industrial roots. Today, like many Connecticut towns, it is mostly suburban.
According to the town's website, Hampton (Windham County) was founded in the 18th century as Windham Village. In 1786, it became an independent town. Today, the town is agricultural and that tradition has deep roots. Industry mostly passed it by, settling in nearby Windham. More recently, the town has intentionally cultivated its reputation for open space and small town living.
So... If you're looking to trace ancestors in East Hampton before 1915, check records in Middletown or Chatham. Hampton goes back a lot further.