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)
Also, SAME codes add in special data for different functions, such as notifications for specific WX, Civil Defence/EMA, LEA, and Official Government alert messages. They all run on the basic FIPS codes, plus the "Status Bit" addition to set off various alerting devices. You can even take a look at the multitude of Alert Status Bit portions on the newer scanners manuals in the sections telling you how to program the multiple WX Functions available now.