Mice are a part of the rodent group, which includes squirrels, chipmunks, guinea pigs and more.
House mice now have many genetic, reproductive, developmental, morphological and anatomical differences. The list below is not exhaustive, but for those with a casual interest it should get you started:
• Genetic differences: Norway rats have 22 chromosome pairs, house mice have 20 (see Levan 1991). Norway rats have 2.75 billion base pairs while mice have 2.6 billion (humans have 2.9). About 90% of rat genes have counterparts in the mouse and human genomes (Rat Genome Sequencing Consortium 2004). See Burt et al. 1999, Grutzner et al. 1999, and Watanabe et al. 1999 for more.
• Morphological differences: Norway rats are larger, heavier and longer than house mice (Norway rat: 350-650 grams, 9-11 inch bodies and 7-9 inch tails; house mice: 30-90 grams, 3-4 inch bodies and 3-4 inch tails). Correlated with this larger size, Norway rat body parts are larger than those of the house mouse — rats have larger ears, feet etc. The heads of Norway rats are heavy, blunt and chunky, house mouse heads are small and sharply triangular with pointed muzzles. Note, however, that Norway rats have smaller ears relative to their heads than house mice.