The mushy devices and central weakness on the Trade dollar at the top are consistent with a counterfeit. The 1795 and 1797 coins are supposed to be Draped Bust dollars. Each year of the Draped Bust dollar was minted with a number of separate dies, each crafted separately, with the letters and stars punched in individually, so each die variety is slightly different. The star and letter positions on your two coins, however, are identical, even though they are supposed to be two years apart. Not only are they fakes, but they were made by the same outfit, who took one template and just change the dates to create more inventory. These pictures I stole from a website that sells a particular Chinese counterfeiter's output in bulk (Act now! They've been marked down from $2.00 to $1.90!). I think they're a good match for yours:






























