Impossible to answer without a DETAILED description of ALL markings.
The Remington model 58 sportsman,semi-auto shotguns are valued at between 110-275 dollars for a gun with a plain barrel.You can add 50 dollars for a model with a vent rib barrel.
They were made from 1936-1940, they are date code stamped (month/year) on the barrel. The location diagram and code table is available on the Remington Society of America.
Don't know for sure which you mean... Sportsman 1930-1947 Sportsman 48 1948-1968 Sportsman 58 1956-1963
How do you identify the model of an old Remington shotgun with ser # 232022
Yes both the 11-48 and the sportsman 11-48 are the same gun. The only difference is the sportsman came standard with a plug to limit capacity to 2+1 to comply with hunting laws.
They made them from 1948 to 1968, they are date code stamped on the barrel. Check the Remington Society of America for diagram/code table.
http://www.remington.com/library/history/firearm_models/shotguns/sportsman.asp Go here.
1910
OK, by finding the Sportsman in an old reference I discover that it is the Model 11C. When I find that model in a newer book, it is indeed built under license from FN using the Browning Auto 5 patent. Suggested value in NRA Very Good condition is $250 and $300 in Excellent.
Remington never made a model 84 anything, unless that's a typewriter or firetruck or something other then a firearm.
Starting in 1921 Remington date code stamped all it's firearms on the barrel. You can look up the details on location and the code table on the Remington Society of America on the Manufactured Date link.