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

This is really two different questions rolled into one.

"Morgan" refers to a particular design of $1 coins issued from 1878 to 1904 and in 1921.

Carson City refers to a mint where coins were made during the years 1870-1893. Morgan dollars were among the many different kinds of coins struck there. They have a small CC mint mark over the DO in DOLLAR on the back side.

Because Carson City generally produced fewer coins than some of the other mints at the time, its coins tend to be more valuable than their counterparts with the same date but different mint marks. That's not a hard and fast rule, though.