SAME codes are based on FIPS codes, but they are not identical.
FIPS codes are five digits long, 2 digits for the state & 3 digits for the county/parish. SAME codes are six digits, by adding a leading zero to a FIPS code you get the SAME code for the identical state/county.
The SAME code set includes many zones that don't have a direct FIPS equivalent, such as the coastal and open water marine zones.
SAME codes that have a leading non-zero digit are large counties that are split into smaller warning areas. For example St Louis County, MN is split into six separate SAME codes (127137, 327137, 427137, 627137, 727137 and 927137)