The .44 Special chamber will accept .44 Special, .44 Russian and .44 Colt (Modern). Your main problem will be what feeds through your rifle! Some of the lever action rifles won't reliably feed cartridges shorter than for what they were made. I've seen some .44 Magnum rifles that would feed .44 Specials, some would not. Some could be tweeked slightly until they will feed .44 Specials with no problems. I seriously doubt that the latter would handle .44 Russian or .44 Colt.
The main reason for shooting shorter cases is with very light loads of smokeless powder, and the differences between .44 Special and Russian are not that great unless you are using loads way below the recommended levels, and that can lead to problems in and of itself!