Peace Silver Dollar Counterfeit/Authentic Comparisons
It's obvious the second Seated Silver Dollar is a counterfeit. The most obvious flaw is the scroll with motto on the reverse, all pre-1866 Seated Dollars didn't have a motto or the scroll on the reverse. So it's important to learn facts about any coin type you're buying.
Another obvious problem, I see, is that the coin appears to be "cleaned" but this is more likely caused by the die being polished to mimic circulation wear. It's a popular tactic among counterfeiters to make a coin look more authentic and to hide incorrect design elements from looking obvious.
Furthermore, this coin doesn't have the word COPY stamped on it's surface, making this particular coin illegal to own. Some might argue that since there's no such thing as an 1847 Seated Liberty Dollar, with a motto on the reverse, then it's just a fake reproduction. Regardless, this coin isn't authentic and is worthless.
SEATED LIBERTY SILVER DOLLARS - GOBRECHT TYPE (1836-1839)
Each silver dollar type above was only minted during these years as shown, but you also must take note of what mint mark was used on each year, and never buy a year that has a mint mark not used for that year. In example, a 1921-CC Morgan Dollar never existed nor does an 1872 Trade Dollar. So know your types, know your dates for each type, and know the mints that minted the coin date for each year.