Both em-dashes (–) and ellipses (…) are used to indicate unfinished thoughts, but their uses differ slightly.
Em-dashes are used to indicate a thought that ends abruptly, either because the speaker ended it that way for effect (“aposiopesis”), or because he or she was interrupted.
I was just about to tell your dad that our math test was --
-- Printed in green ink! Can you believe that? Green ink? For a math test?!
Ellipses are used to indicate a thought that trails off.
And you’re telling me this because...?
Both marks have other uses as well. For example, em-dashes are also used to set off certain dependent clauses, and ellipses are also used to indicate that a part of a quote has been omitted.