googling "site:imdb.com ..." uses google's index, restricted to imdb.com; DDGing "!imdb ..." uses imdb's internal search.
I almost never bother with sites' internal searches, as google's "site:" feature almost invariably works better, so I wouldn't be inclined to use DDG's site-search bang-lines myself. YMMV, I guess it depends on how good the site in question's internal search functionality is.