Is there a difference between the Morgan dollar and the new Orleans dollar?

That's an Apples and Oranges question. The terms describe very different things.

"Morgan" refers to the design used on dollars minted from 1878 to 1904 and in 1921. They were designed by George Morgan.

"New Orleans" refers to the mint where some dollar coins were struck during the years 1846-1860 and 1879-1904.

So, to sound like one of those questions on a high-school standardized test,

> Some Morgan dollars were made in New Orleans

> Some dollars made in New Orleans were Morgan dollars

> Many Morgan dollars were not made in New Orleans

> Some dollars made in New Orleans were not Morgan dollars.