American citizens get married and get a green card for naturalization.

1. From the day you get a conditional green card, if you still maintain this marriage, the immigration office will send you a form two years later.

Your citizen spouse should sign it and send it back to the immigration office. In a few days, you will become an official green card.

2. Marriage immigrants who marry citizens can apply for naturalization examination within two years and nine months. Sometimes, as you said, you apply for the naturalization test before your green card arrives. When they are accepted as citizens, the green card will arrive, which is useless at all (I was like that).

The five-year citizenship test is the waiting time for getting a green card except for marriage immigrants.