The person who holds a Green Card is a "Permanent Resident" that is the title of a green card holder. That means that tax wise the green card holder is treated the same as a citizen.

The short answer is no. They are not the same. Green card holders do not have the same freedom to leave and re-enter the US as US Citizens do. A green card holder always runs the risk of being denied re-entry where as a US Citizen typically does not have to worry about returning to the US. Additionally, a green card holder can possibly learn that they have lost government benefits (such as welfare) after returning to the US. Green card holders are not eligible for a US Passport nor can they vote. A green card holder can apply for citizenship after having the green card for at least 5 years, but they will need to have good moral character and be able to pass a history and government exam. It is also a must that the applicant speak, read and write English.

Green Card holders are deemed to be U.S. tax residents under the Internal Revenue Code. In most circumstances Green Card Holders are also treated as U.S. tax residents under U.S. tax treaties.
U.S. Green Card holders have traditionally been able to use tax treaties to sever “tax residence” with the United States. This decision carries both burdens and benefits and should never be undertaken without competent professional advice. (For Green Card holders who are “long term residents“, the use of a “tax treaty tie breaker” will result in expatriation. Expatriation may trigger the imposition of the Sec. 877A Expatriation Tax.)
Read full article: www.taxconnections.com/taxblog/in-the-21st-century-the-most-important-thing-about-a-person-is-tax-residency/