The American Silver Eagle is a coin worth one dollar. It is an official bullion coin, meaning it is stored for its value and not traded in regular commerce. The coin is 99.9% silver, with an image of Walking Liberty on one face and the titular eagle on the other.
The 1900 Morgan Silver Dollar features the Statue of Liberty on one side, and an eagle on the other. Online collectors are buying Morgan Silver Dollars for around 100 to 300 dollars, depending on quality.
A Morgan silver dollar is a large dollar coin, on the front there should be a depiction of Lady Liberty's face wearing a small crown saying "LIBERTY" on it the reverse features an eagle with olive branches and arrows and a wreath at the bottom. They were dated 1878 to 1904 and also made in 1921. The only other coin that could be easily confused with a Morgan dollar is a Peace Dollar of which some were also minted in 1921, they have the same size, but the liberty on a Peace dollar looks like there are rays coming out of her head and the reverse of a Peace dollar has an eagle perched on a rock engraved PEACE.
The 1922 is probably a peace dollar. It would have the word peace on the side with the eagle. The 1921 is probably a Morgan dollar. It has a Liberty head on one side and an eagle on the other. These are worth about $25-35 on average.
You have one troy ounce of 99.9% pure silver. Current value about $16. BUT I GUESS THIS IS NOT SILVER If the word PEACE is under the eagle, you have a standard-issue dollar coin made of 90% silver. Its value is around $16 depending on the price of silver.
Chief Engraver Charles E Barber designed a Liberty Head series for dimes, quarters, and half dollars, 1892-1916. Miss Liberty was on one side. The other side of the dime had a wreath, that of the quarter and of the half-dollar an eagle.
That's NOT the Statue of Liberty, because the statue wasn't built until 1886. What you have is a Morgan silver dollar. If the date is so worn that you can't determine the last number, then based on that condition, the coin's value is only for the silver content. As of 23 January 2013, it's worth about $25.
The Walking Liberty Dollar, better known as a Silver Eagle is a US bullion coin. On the obverse (heads) it features a woman personifying liberty, in her hand she has an olive branch and her other hand is outstretched to the sun. Flowing in front of her is an American flag. This is the same obverse (heads) design that was used on the Walking Liberty Half Dollar. On the reverse (tails) it features an eagle with its wings spread, olive branches grasped in one foot and arrows in another with stars above it. It says above the stars "UNITED STATES OF AMERICA" and below it "1 OZ. FINE SILVER ~ ONE DOLLAR". They are worth generally the price of silver in the coin (with usually a dollar or two added because of the fact it is a coin) which is always higher than the one dollar face value.
You're describing a 1923 US Peace dollar, called that because it was struck to commemorate the end of WWI. There's more information at the question "What is the value of a 1923 US silver dollar?"
The biggest difference is Peace dollars exist and Liberty dollars don't. A very common mistake non-collectors or amateurs make with US silver dollars is they think because the word LIBERTY is on the obverse of a Peace dollar (or other coins) it's called a liberty dollar. No US coin is referred to as just a "Liberty" coin. Also this comes up with Morgan dollars, but with the national motto E PLURIBUS UNUM because it's on the front of the coin.
A silver dollar can feasibly mean at least three different coins. From 1840-1873 the Seated Liberty dollar was minted. It depicts a seated woman (an idealized Lady Liberty). From 1878-1921 the Morgan silver dollar was minted. It features again Lady Liberty, modeled after a school teacher named Anna Williams. From 1921-1935 the Peace silver dollar was minted. It was designed by Anthony de Francisci to represent Lady Liberty modeled by his wife Teresa. Other commemorative silver dollars have been minted since, but after the 1930's and 40's real silver dollars came out of circulation. These three are probably what you are asking about.
If your (walking liberty half dollar) coin is dated 1916 (and some 1917 coins) the mintmark is found underneath "In God we Trust" on the front of the coin. All other years the mintmark is found on the reverse of the coin to the left of the branch that the eagle is sitting on. Keep in mind that if your coin has no mintmark, it was minted in Philadelphia. If you have a silver eagle dollar which also uses the walking liberty design, the mintmark will be on the back under the olive branch that the eagle is holding. Bullion silver eagles do not contain mintmarks and could be minted from a number of different mints depending on the year the coin was issued.