En México: calzones, chones, choninos (términos usados indistintamente para las prendas masculina y femenina, el segundo es un eufemismo del primero), jaulas o pantaletas (si es muy delgada por detrás, tanga).
It's chones, and it's not derogatory nor vulgar, as far as I know. It's just slangy, such as the English terms for underwear like undies, or (for older generations) shorts. Edit: also knickers.
caerse los chones: quedar azorado, sobresaltado por la sorpresa.
chones n.pl. underwear, especially undershorts or panties. Also chonies, choners. Editorial Note: Despite its proximity to a mention of lingerie, chonies in the 1928 citation is probably a typographical error for chorines. Etymological Note: (Mexican) Spanish slang chones, perhaps from the Mexican Spanish calzones ‘underwear’ or less probably from the English long johns. The Oxford English Dictionary includes a 1717 first citation for poncho from Frezier’s Voyage to the South Sea in which Chony appears; however, it may be unrelated: “The Spaniards have taken up the Use of the Chony, or Poncho…to ride in, because the Poncho keeps out the Rain.” (source: Double-Tongued Dictionary)
bragas is not for mexico. None of my mexican friends have heard of that word. They use calzones for women and calzoncillos for men, and other slang words like chones etc..