An "uncirculated" coin is a coin that has never been in circulation and has none of the little dents and scratches on it that you would expect on a circulated coin.
A "mint uncirculated" coin is a coin that has never been in circulation and is still in the same condition (and packaging) that it was in when it left the Mint.
A "Proof" coin is one that is struck on specially prepared and polished dies giving the coin a brilliant finish.
A "Proof FDC" (Fleur du Coin) coin is one that is struck on specially prepared and polished dies, and the coins further hand finished giving the flat surfaces of the coin a mirror like finish.
A "Matt (or Matte) Proof FDC" coin is one that is struck on specially prepared and polished dies, and the coins further hand finished. On modern coins, the highlights would be finely granulated giving the coin a sharp contrast between the flat surfaces and the image. On 19th century coins, the surface might have been finely granulated giving the coin a sharp contrast between the flat surfaces and the image.
All variations of Proof coins are significantly more expensive to buy when issued due to the extra work involved in producing them. Also Proof coins can be made from the usual metals or, as often as not, precious metals such as silver and gold, increasing the purchase price even further.
Most Proof coins, especially those made from precious metals, would be sold with a "Certificate of Authenticity" or some similar certification from the Mint concerned attesting to the fact that the coin is made from 22 carat gold or 0.925 sterling silver, for example.
You can't unless you pay the $20+ to send your coin to NGC/PCGs even under magnification the ordinary person cannot tell the difference between a pf69 and pf70 coin. Of course, it is easy to tell if your coin is uncirculated or proof, a proof silver eagle will have very shiny, mirror like fields that are easy to see yourself in. An uncirculated silver eagle will be shiny, but won't be mirror like. Also, the raised part of the coin will look frosted on a proof coin but not on an uncirculated coin.
Uncirculated coins go through the normal minting process, but are then removed and placed into sets for collectors. Proof coins are made on specialized dies to achieve better detail and more shine in the finish.
Uncirculated coins are ordinary coins that were struck for use in commerce but haven't been spent yet and have no wear. Sometimes you can be lucky and get a roll of uncirculated coins from a bank. Most Mints around the world also sell uncirculated coins to collectors; they're in sealed packages with some form of indication that the coins were never spent. Proof coins are specially struck for collectors. They're made separately from ordinary coins using highly-polished blanks and dies that produce extra-sharp, very detailed images. Many proof coins have mirrorlike surfaces but others receive special treatments that give a "frosted" appearance to the raised parts of the design or the background.
Circulated means the coin has been handled and used. Uncirculated is a coin that hasn't been spent, and is often fresh from a bank roll. Proof is a special strike technique resulting in an extra clean and shiny finish to the coin, and is made specifically for collectors.
The American Eagle Gold coins are made in Uncirculated and Proof versions. Circulated means exactly that, it has been circulated and or used. We do not use any gold coins at all in every day business. Proof coins have a highly reflective, mirror-like surface. The surface of a uncirculated coin does not.
If the coin has an "S" mintmark it's Proof, if not, it's the uncirculated version. Current average retail value for a Proof coin is $40.00 Uncirculated is about $29.00.
Depending on the condition, an Eisenhower uncirculated dollar as a value between $10.00 and $20.00, of 2014. The 1971 S Silver Proof is worth the most.
A frosted proof coins were issued by the US Mint prior to 1936. In appearance they have a mirrorlike field [[the field of a coin is the flat areas not covered by the design]]with the design of the coin appearing to be frosted or dull in comparison to the field. This type of proof was again used on proof coins in the late 1970s and are refered to as "cameo" proofs. A mirror proof [[also called a Brilliant Proof]] has a mirrorlike surface over the entire coin. This type of proof was issued by the Mint from 1936 until sometime in the late 1970s.
A proof uses postulates and theorems to prove some statement.
A deep Cameo coin is a numismatic term used to describe a proof coin that exhibits a very high level of contrast between the frosted design elements and the mirror-like fields. These coins are highly sought after by collectors for their stunning appearance and sharp detail.
1975 Proof sets are valued at $11.00.
These coins are still potentially in circulation so, unless they are part of a Proof or uncirculated mint set or are individual Proof or uncirculated coins and in absolute mint condition, they are worth Two Pence.