First, no US coin of any type is referred to as a "Lady Liberty coin", but the symbolic portrait of Lady Liberty is on most older US coins such as the Morgan Dollar series. So the Morgan and the lady liberty are the same coin.
A Morgan dollar IS a silver dollar. The term Morgan refers to the designer George T. Morgan who created the images used from 1878 to 1904 and in 1921.
All Peace dollars have the same design. The difference between the 1921 Peace Dollar and the 1921 Morgan dollar is that Liberty looks completely different. In the more common 1921 Morgan dollar, Liberty wears a crown with the word "LIBERTY" on it, on the reverse of the Morgan dollar, there is an eagle with olive branches and arrows in its talons along with a wreath under it. On the Peace Dollar, Liberty looks like she has rays coming out of her head and on the reverse there is an Eagle sitting on a rock inscribed "PEACE", there is no wreath on the reverse.
It is a representation of Lady Liberty.
Money can have various values based on condition and certain stamping. An 1885 Morgan Liberty Head silver dollar can be worth between $20 and $400.
The coin is referred to as just a "Morgan dollar" all silver dollars have "Miss Liberty" on them. An 1882 Morgan dollar is very common, circulated coins are $30.00-$37.00.
The image on the face of the Morgan Dollar is a rendition of Lady Liberty designed by George T. Morgan.
On the front of a Trade Dollar it has Lady Liberty seated facing the left and on the back below the eagle TRADE DOLLAR. A Morgan Dollar has the head of Lady Liberty on the front.
There's no difference. All silver dollars minted in 1894 used the Morgan design, named for the famous designer George T. Morgan.
The figure portrayed on the obverse of the Morgan silver dollar is Lady Liberty who is a non existant person used to represent Liberty.
Miss Liberty, as in "Statue of ..."
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.