Application for Travel Documents I-131
A Re-entry Permit is applied by permanent residents or conditional residents, it is used to allow admission to the United States upon returning from abroad, without the need to obtain a returning resident visa. For example if you or someone who is traveling abroad on a Green Card will be staying for more 8 months. A reentry permit will allow you to stay up to 2 years abroad and return to the U.S without any issue.
Refugee Travel Documents
A Refugee Travel Document is only issued to a person in valid refugee or asylee status, or to a permanent resident who obtained such status as a refugee or asylee in the United States. The Refugee Travel Document must be obtained by a person who holds asylee or refugee status and is planning to travel abroad. A Department of Homeland Security Office at the port of entry will determine your admissibility when you present your travel document.
Advance Parole Documents
The Advance Parole Document allows aliens to physically enter the U.S. Even after the issuance of the parole document, the “parolee” remains and applicant for admission at the time of entry. DHS (Department of Homeland Security) may revoke or terminate your Advance Parole Documents at any time, including while you are outside of the U.S, in which case you will need to have a valid visa to return to the U.S. If you have applied for adjustment of status then you must apply for an Advance Parole Document, You will be deemed abandoned if you leave the U.S without that document.