I remember this confusion that I had before I was given the close-vote priviledge. Since I can't show it on this site, let me use BioSE's flagging (where I don't have close vote):
Apart from them being in two different locations, what do the two different duplicate buttons do? Is there a difference between flagging as a duplicate and flagging to close as a duplicate that I'm not aware of? Or was it possibly just a redundant mistake on SE's part? Or possibly kept in both columns just for a sense of completeness?