It's the "permanent" bit. Being an asylee or refugee isn't necessarily a permanent status - like if your home country gets out of a civil war or a coup leader ends the coup and goes into exile, you no longer need to fear for your life if you go back.

> If you are a refugee, you are required by law to apply for permanent resident status 1 year after being admitted to the United States in refugee status. If you are an asylee, you are not required to apply for permanent resident status after being granted asylum for 1 year.