Types
Uncirculated coins generally have some imperfection that would cause them to be withheld from general circulation. Proof coins, on the other hand, are coins specially created for display or collectors.
Features
Uncirculated coins can have dings or scratches or some type of blemish that disqualifies them from being released. Proof coins are highly polished and are in pristine condition.
Identification
Proof coins will also have greater contrast between the raised portions and the flat portions. Also, the raised portions will be slightly more visible than in uncirculated coins, because of the way in which proof coins are created.
History
Proof coins were originally produced for a select few. But that universe was expanded in the 19th century, when coin collecting began to become a popular pastime.
Potential
Proof coins are considered to be the better investment, because they are usually valued more greatly than uncirculated coins. That might not pertain, however, to uncirculated coins with some notoriety.