As far as I know, the Chilean Mausers were all 7x57. To be 100% certain (and to make certain the chamber wasn't reamed out to fire some other cartridge), take it to a gunsmith have have them take precise chamber and bore measurements.
Some Mausers
Check the related link at the bottom. There were several variants of the Mauser rifle, and I can't give a link to a specific article without knowing which model you have. There's a menu on the left hand side which has articles for different variants of the Mauser (and several other types of rifles).
2 different pistols that use 7.62mm ammunition are the Czech-made CZ-52 and the German-made Mauser C96. Many other pistols use variations of the 7.62mm round, but the two listed before utilize true 7.62mm rounds.
More information is necessary. If the rifle has a 4-lug bolt head, it is the same as a Mossberg 810. Research the 810 for info on this rifle. It may be made on FN Mauser 98 actions, in which case it will be like any other Mauser 98 sporter. Otherwise, it will be German made by Heym and is either the same as a Mauser 2000 or Mauser 3000 action. The scope, on the other hand, is almost impossible to describe these days. It will likely have Japanese optics.
anders = different, differently woanders = elsewhere
The Mauser Gewehr 98 was created and produced around World War I. Often times, people will say M98 to denote the Gewehr 98 or K98k. This is true because they are referring to the basic design. On the other hand, Mauser is currently producing some new, modern versions of the Mauser 98 action. This model is known as the Mauser M98. Hope this helps.
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Not knowing how many variations of the Chilean Mauser were made, or which variation you're referring to, the assumption will be made that you refer to the Mod. 1908, which was a variation of the German Gewehr 98 Mauser. This stock, and stocks of other variants (such as the Argentine Modelo 1909) should have some degree of interchangeability with the Mod 1908, although it is possible that some sanding or other minor alteration will be necessary.
Depends on the time period and the type of gun. During WWI, the main German infantry rifle was the 1898 Mauser. The main American rifle was the 1903 Springfield. Their designs are so close that US had to pay royalties to Mauser. US Army also made use of shotguns for trench warfare, while no other country did so. In WWII the standard German rifle was the Karabiner 98, which is still the same Mauser design. US was armed with the M1 Garand, which had higher ammunition capacity and a faster rate of fire that made it superior. WWII also saw the use of many other types of weapons, but in more limited numbers. Some of them had no direct counterparts on the other side of the conflict, such as the M1 Carbine. In pistols, German gun design has always tended to be more mechanically complex, where American gun design is more on the functional side.
The 7mm Mauser is generally considered short action. 7x57 is shorter than 30-06. OTHER 7mms are different lengths.
Desgin specifications.