Adjustment of status allows the married spouse of a U.S. citizen, who was “inspected and admitted” or “paroled” into the United States, to apply for permanent resident status without having to leave the United States.
A “green card” is proof of your lawful permanent resident status in the United States. It allows you to live and work in the U.S. without any time restrictions whatsoever.
If you obtain your green card through marriage to a U.S. citizen, you qualify to apply for U.S. citizenship three years after you are approved for lawful permanent residence (assuming you stay married to the same person).
After you apply for adjustment of status, you receive temporary employment authorization while your application is being processed. You may also be eligible for a travel permit which would allow you to travel in and out of the United States during this time.
Once you become a permanent resident, you can work for any employer in the U.S. for any length of time. The “green card” serves as proof of employment authorization. You can also freely travel in and out of the United States using your passport and green card. However, you have to be careful not to “abandon” your permanent resident status by staying outside the U.S. to long periods of time.