Proofhouse.com has sn's for Colt and Winchester. Browning and Ruger have a sn search function on their sites.
The letter on the serial number usually indicates the date it was made. The letter "S" on your serial number indicates that it was made on 1965.
1929 if a 38, 1937 if a 32.
@1960
1960
1920
year 1974
@ 1965
1970
Generally Stevens and Savage shotguns work like this: A for 1949, B for 1950, C for 1951 etc. You can go to www.bluebookinc.com and look it up to be sure. It is free to look up the serial number/date of manufacture.
If you contact the manufacturer and give them the serial number and model they will be able to tell you.
A serial number without a manufacturer is meaningless. That number for a Bach is going to have a different date than the same number on a Holton or Conn.
1977