In the Genki I textbook, they seem to reference the present perfect tense three times, but each with a different grammar. Here they are, with book-style English translations:
日本に行っています。(Ch 7, 〜ている form)
I have gone to Japan.
日本にもう行きました。(Ch 9, simple past form with もう)
I have already gone to Japan.
日本に行ったことがあります。(Ch 11, 〜ことがある form)
I have had the experience of going to Japan.
I'm not really sure about the semantic and grammatical differences between the three, even in English (although the translations may be imperfect). How can I understand them in relation to each other?
Also, does it ever make sense to combine the forms? Like,
I have already gone to Japan (?)
I have already had the experience of going to Japan (?)