Its a SPORTSMAN. It says so on the breech bolt. I don't think I've ever seen a Sportsman breechbolt used to replace a Model 11 breechbolt but maybe it could happen. However the pheasant rollmark on the breechbolt side of the reciever is of a pheasant on the ground, and that's definitely a Sportsman rollmark.
Model 11 breech bolts are stamped MODEL 11. The pheasant scene rollmark on a Model 11 is different than on a Sportsman. The Model 11 rollmark is of a flying pheasant.
Interestingly, identical-looking flying duck rollmarks are found on the opposite side of the receiver from the breechbolt rollmarks on both guns.
In addition to these things, the original wooden forearm on a Sportsman is different (it's flatter) than the original wooden forearm on a Model 11. I think the Sportsman forearm style was called a "beavertail". Some liked it better. Some didn't. I've owned both. I didn't care. The magazine cap is different too. Google a Model 11 and look at the forearm and the magazine cap and compare it to your Sportsman and you'll see the difference.
The most important difference it the Model 11 and the Sportsman is that they have different ammo capacities. Model 11's hold 4 shells in the magazine and 1 in the chamber for a total capacity of 5. (Due to some states hunting regulations, Model 11 magazines are sometimes temporarily plugged to accept only two rounds, giving a total capacity of 3 like the Sportsman, but the plug is removable and anytime you want to go back to a 5 shell capacity you can.) The Sportsman model was made to only hold 2 shells in the magazine; no plug is required to give it a maximum capacity of 3. That's all it will hold, Limiting the capacity like that was supposedly done as a sop to sporting men and conservationists who objected to hunters using 5 shot autoloaders for hunting. I guess they never thought of bag limits back then. The capacity reduction to 3 still gave the Sportsman Model a 1/3 firepower advantage over a double-barrel gun
In good condition with uncracked stocks and forearms, either of these guns are still great hunting guns and at the dirt cheap price they sell for these days every home should have one. But magazine capacity is an important consideration especially for people who own only one gun, an all purpose shotgun that's used in part for home defense. (In a place like Alaska, you probably need something for bear defense too.) For either of those purposes, I'd prefer a 5 shell capacity. I'd pay no more than about $150 for a 12 gauge Sportsman in good condition because of its limited capacity. Well, if it was in great condition I might go to $175. I'd probably pay $250 tops for a 12 gauge Model 11 in very good condition. Those would be great prices for an autoloading shotgun in good condition. A 16 gauge might go a shade higher than that. I don't know. They're a little rarer, but personally, I'd have no use for a 16 gauge gun.
PS Logs gun has a different safety of the type utilized on on early Model 11's. Not for nothing were they called suicide safetys. I've read that Remington stopped making the kind of safety Logs has in 1928. (Interestingly, FN Browning A-5's which are nearly identical to Remington Model 11s kept that old style suicide safety through about 1939.) But after 1928 Remington went to the safer button behind the trigger.