What's the difference?
I've already seen Terminator.
I've seen Terminator before.
They arrive at propositions with the same truth conditions, but by different means; and with somewhat different contextual expectations. In fact, they arrive at the truth value of the sentence without them. They both mean:
When that is true, both of the sentences are also true (when else could you have seen it that wasn't before or already?), and when that is false, both of them are false; and vice versa, in all combinations. They're synomymous. All of them. That's mostly because they all use the Perfect construction.
Adverbials like before, already, never, etc. are used to add nuance and build the background context. Language does that a lot; there's almost never just one way to say something.
Semantically, the before clause is a simple Existential perfect, "used to indicate the existence of past events", and emphasizing the pastness of the event with a redundant before (when else could you have seen it?).
The already clause, however, has a more complex semantics. Already presupposes expectations on the part of the speaker about the timing of events; normally one uses already to refer to events that occur before they are expected to
So, either before and already might be used in a case where the speaker classifies seeing Terminator as an event that, like registering to vote or getting married, need not be performed more than once. But the one with already is quite definite, in my opinion, that the speaker is not interested in seeing it again.
I think the second one is more likely to count as a No answer. Of course, that could be just my perceptions; there's a lot of room for individual variation here.
Already, in the other hand, is an adverb.
In theory, both already and before could be used in their adverbial form to modify seen in the examples given, and would be correct.
However, at least in US, before, in its adverbial form, is more often used in referring to location or action rather than viewing something.
When referring to visual experience, before just doesn't seem comfortable.