An alien number is a unique 7, 8, or 9 digit number assigned to a noncitizen by the Department of Homeland Security upon the creation of a file.
An admission number is the number on a CBP Form I–94 or CBP Form I–94W, the arrival/departure form Customs and Border Protection (CBP) gives most nonimmigrant aliens when they arrive in the United States. While most nonimmigrant aliens will automatically receive an admission number when they enter the United States, Canadians will not. However, if a Canadian asks a CBP official for an admission number when they enter the United States, they will be given an admission number.