Rodent taxonomy is confusing, as far as I can tell:
Most typical mice and rats belong to the family Muridae in the order Rodentia, specifically in the suborder Myomorpha(mouse-shaped). The other suborders of Rodentia are Sciurimorpha(squirrel-shaped), Castorimorpha(beaver-shaped) and Hystricomorpha(porcupine-shaped).
The problem is that rodents don't actually have names that fit their category, so you have for example:
- dormice and mountain beavers who are squirrel-shaped, but not spiny or pygmy dormice, those are mouse-shaped
- kangaroo rats/mice who are beaver-shaped
- rock rat is a name for like 6 different species, of which half are porcupine-shaped. Rock mice are mouse-shaped though
- moonrats are related to hedgehogs, who aren't rodents
- all mole-rats are porcupine-shaped, but naked mole-rats are part of a different family than all the other mole-rats, moles aren't related to them, but they are in the same order as hedgehogs
- similar deal with chinchillas and chinchilla rats, both porcupine-shaped, but different families.
- shrews aren't related, they're related to hedgehogs, but treeshrews are a sister order to the one containing lagomorphs and rodents
- bats? not related to any of the above, they're a sister clade to Eulipotyphla, who are the hedgehogs and moles and shrews I mentioned
- tenrecs, elephant shrews and golden moles aren't part of that group, they're related to elephants