In the UK, the old word “gotten” dropped out of use except in such stock phrases as “ill-gotten” and “gotten up,” but in the US it is frequently used as the past participle of “get.”
Sometimes the two are interchangeable, however, “got” implies current possession, as in “I’ve got just five dollars to buy my dinner with.” “Gotten,” in contrast, often implies the process of getting hold of something: “I’ve gotten five dollars for cleaning out Mrs. Quimby’s shed” emphasizing the earning of the money rather than its possession.
Phrases that involve some sort of process usually involve “gotten”: “My grades have gotten better since I moved out of the fraternity.” When you have to leave, you’ve got to go. If you say you’ve “gotten to go” you’re implying someone gave you permission to go.
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