What is the difference between a Morgan Carson City Silver dollar and a Carson City Silver Dollar?

One group is a subset of the other.

"Morgan dollar" refers to the design by George T. Morgan that was issued from 1878 to 1904 and again in 1921.

Carson City refers to one of the mints where dollars were struck. The Carson City mint operated from about 1870 to 1893, and it struck Seated Liberty design dollars, Trade dollars, and Morgan design dollars.

The Morgan design was also minted at Philadelphia, San Francisco, New Orleans, and Denver.

So ... a Morgan Carson City dollar is one that was struck between 1878 and 1893 at the Carson City Mint. But not all Morgan dollars were struck at Carson City, and not all dollars struck at Carson City are Morgans. (see Venn diagrams in high school math!)