The U.S. Federal Census is taken every 10 years on a designated census day by an "enumerator" in a specific area called an enumeration district. The first census was done in 1790; there are no censuses before 1790.
The Family Group Sheet identifies a couple and their children. Everyone with a spouse or child has two group sheets; one as a child with parents and usually one as a parent with children.
Digital copies, sometimes called "portable files", are copies of your original documents, family group sheets, notes, pedigree charts, etc.
In 1820 the Federal Government began requiring ship manifest lists but the early years can be difficult to locate.
The census records may contain a good clue to when a person obtained citizenship.