Your Mexican 1910 rifle is a M98 pattern rifle, any 7X57mm/7mm Mauser ammo you feed it will be fine.
7X57mm is the correct name for the cartridge in question. It is also called 7mm Mauser ( because of the firm that designes and marketed the rifles in that chambering), or sometimes just 7mm, although this last one confuses a lot of folks because there are several 7mm cartridges (7mm Remington Magnum, 7mm Weatherby Magnum, 7X61mm Sharpe & Hart, and so on, ad nauseam). The reason your particular rifle is marked 7mm is because that was what the cartridge was called by the Mexican army, and it replaced a number of older black powder carridges as well as lances and machetes (I am serious and not being derogatory of our neighbors to the south).
Never try to educate someone who resists knowledge at all costs.
But what do I know?