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These three terms, while all resulting in the individual no longer having a green card, are different in terms of who initiates the process, the basis for initiation, and to some extent the future impact on being able to enter the US again.
Anyone with a green card can surrender it as a matter of personal choice. There’s no real limitation on doing this other than needing to do so at a consulate outside of the US (otherwise, there would be no legal status immediately after surrendering). There’s a form for this process, the I-407. The procedure differs depending on consulate; some allow this to be mailed in, some require in-person appearance. Someone who has surrendered a green card can still be eligible to enter the US on a nonimmigrant visa in the future if they otherwise meet the criteria of the visa they’re requesting.
Revocation is where USCIS or another US government agency (for instance, the Department of State) either finds fraud in an application or petition after the fact, or finds some other reason why the application or petition couldn’t or shouldn’t have been approved.
Before approval of a green card, an immigrant petition (an I-130 for a family member or an I-140 for an employee) can simply be administratively revoked by USCIS (they would first issue a Notice of Intent to Revoke, and there would be an opportunity to argue it with them before any action became final). After a green card is approved, though, revocation of permanent residence requires removal proceedings in immigration court.
Revocation is a government action, as opposed to surrendering which is an action by the card holder. Depending on the reason for revocation (fraud vs some simple mistake of fact regarding eligibility for instance), a person having a green card revoked might not be eligible to come back as a nonimmigrant.
Abandonment is a government determination based on their perception of an individual’s intent to abandon the green card. The determination is based on the green card holder’s maintenance of “ties” to the US (and often lack of ties elsewhere).
People often discuss ties to the US only in terms of time spent in the US vs time spent abroad, and that is the most common and obvious “tie” the government looks to – but it isn’t the only one. They can also look to failure to pay US taxes, filing taxes as a “nonresident,” or actions abroad evidencing resettlement in another country (serving in a foreign government or military, for instance).
With regard to not physically being in the US, there are some clear definitions at the low and high end, but not so much in the middle. Absences of six months or less aren’t usually a problem. Absences of a year or more usually ARE a problem: there’s a legal presumption of abandonment for absences of over a year, though this can be overcome with solid enough evidence (though the best option is to apply for a “reentry permit” before leaving, permitting absence from the US for up to two years without abandonment). Absences between six months and a year are a very grey area and are entirely dependent on the evidence – someone abroad ten months but who maintained a home and assets in the US during a provable short-term work assignment may have less of a problem than someone who completely moved their home, assets and work abroad for only seven months.