As an adjective, generalized means something involves many things, people, or parts, not just one spot. A generalized fear is not fear of one dog; it is a wide, fuzzy fear. A generalized statement talks about a whole group. In medicine, a generalized illness or rash has spread through the body, rather than staying in one place (local or localized). Though actually, English also uses generalized as the past form of the verb generalize: ‘She generalized from one example.’ That sentence is about making a wide claim. The adjective sense is about how spread-out something is. American spelling keeps the z (generalized); British books may write generalised. Formal writing and doctors like this word; everyday talk might just say ‘wide’, ‘all over’, or ‘not just one’.