What is the difference between
As far as I can tell they provide basically the same functionality.
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I never used iedit extensively, so I could be unaware of some of its features, but basically iedit is a more interactive search and replace: you can select occurrences of a string in some scope (region, defun, buffer, etc.) and then replace them with something else.
Compared to that, multiple-cursors generalizes in two directions, the second much more important than the first in my opinion:
You are not limited to put cursors just at occurrences of some string. You can put cursors wherever you click the mouse, or at the end of a bunch of lines, or at matches of a regexp, etc., or any combination of these locations.
Even if you did choose to place cursors just at occurrences of some string, you are not limited to just replacing them with some other string. You can do any Emacs text editing simultaneously at every location. For example, you could transpose the words found around each cursor, or mark the entire defun containing each cursor and comment it out.
Just as iedit can be thought of as an instant-preview version of query-replace, multiple-cursors can be thought of as an instant-preview version of keyboard macros.