In the Movie Col Pattersen used a sporterized Enfield No. 1 action with a 5 round magizine.
Later in the movie he used the Doctors rifle that I believe was a Popular English falling block at the time. The name excapes me, I think it starts with an F. I want to say Frazier but it think that is wrong. It was the rifle that Bill Ruger based his No1 on.
While Col Pattersen was a real person the Hunter Remington was not. If the book the Man eaters of Tsalvo, Col Pattersen talks about many hunters that came to help deal with the maneaters.
His guns were an English Howda in 16 ga (popular at the time with tiger hunters as a last ditch gun if a tiger got on top of the Asian elephants they hunted from) The Side by Side is any number of Side by side rifles that are or were popular, in one of the nitro express rounds like 470, 500 or 577 Nitro Express. It also could be a Bore like 12 or 10 bore side by side rifle. For that matter it could have been one of the CVA 20ga rifles. I saw a similar rifle to the one in the movie with a smaller hole not too long ago in 400/450 3" (400 Jefferies) for $15,000.
Samuel at one point has a standard Side by Side game in 12 ga and can be any of the English or Irish makers. (Purdy, Holland & Holland, Churchill, William Moore...........) As far as a movie gun it could be Spanish, Italian, or Turkish.