The Swede one is an original commercial Mauser sporter. It is full-stocked in the style later called "S-type" with double "Schnabel" on the foreend. Otherwise the stock is Mauser factory pre-1913 commercial style. Jon Speed shows photos of two such rifles in his book "Original Oberndorf Sporting Rifles", page 120. The small tangent rear sight was never used on any military Mausers, but was quite popular on early sporters. The same sight, with different range numbers, was also used on many .22 Mausers and on the C96 pistol. Also note the lever-release deep magazine floorplate, used only on 10.75x68s by Mauser.
The Peterlongo rifle is a custom job by a good gunsmith, apparently based on an ex-military action. Except for the calber, not very remarkeable.