What is the difference between ‘Duplicate’ (from the ‘manipulate’ group) and ‘Copy and transform’ (from ‘utility’ group)?

It looks like there's no difference, apart from what you'd type to get them using the keyboard.

In earlier versions, there was a separate Duplicate node, and it behaved in a way that was subtly, sometimes problematically, different from the old Copy node. For example, in old Duplicate SOP, if you set the number of copies to 4, there would be 5 total copies of the geometry, the original one and 4 more, but the old Copy SOP with the number of copies set to 4 would yield 4 total copies of the geometry, as most people expected. Now, people can still type Tab > “du” > Enter to get a node that copies geometry, but it's now consistent with the Copy and Transform node… because it is the Copy and Transform node.