Still not sure if I know what constitutes "queso rallado" and whether there is a word for "grated cheese", and now I'm starting to question whether for some people there is an overlap between "grated" and "shredded" cheese in English.
My teacher was like, "rallado is the one you do with parmesan" and then showed a picture like the first one, which, to be fair, also looks like some of the GIS results for "grated cheese", whereas when I think of grated cheese I think of something much finer, like the second one.