These two statements amount to the same thing, but there is a subtle difference.
If you start watching a film together with a friend, and your friend says, 'I've seen this movie before', the implication is that this isn't necessarily a problem. Your friend may be happy to carry on watching. Perhaps they enjoyed it so much the first time that they want to watch it again.
But if your friend says 'I've already seen this movie', the implication could be that they're going to suggest that you stop the film and watch something else instead. The adverb 'already' suggests that a goal of some kind has been achieved, so it's no longer necessary or desirable to do this. If you've already done something, you no longer need or want to do it. Maybe it's the type of movie that nobody wants to see twice.