Both uses are possible: "While the gifts may have changed over the years, the message behind them is no doubt the same". "May have changed" expresses possibility here. "The pilot may have pressed the wrong button which caused the plane to dive".
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Hans51Thank you so much so 'may have p.p' also can be used for a happening from the past to the present (the first example) and a past happening a speaker guessed (the second example) , right?Yes Hans51