Both words mean “illness.” 病 (n.) means “a particular disease”, e.g. heart disease, neuropathy etc. 病(v.) means “to be ill.” 疾病 (n.) is a general term for ailment, which is more formal and can be used figuratively. (1)我生病了,需要在家休息几天。 (2) 他因病请假两天。 (3) 他病得很严重。 (4) 冬天来了,要防止呼吸道疾病的发生。
疾病 here is a general term.
One can usually say 一种疾病(a kind of illness) or 某种疾病(an illness), which sounds rather formal. When it is used figuratively, one can say: (5) 犯罪是一种社会疾病。
Moreover, 有病 (to have an illness), 得病 (to have gotten ill 患病( to have gotten ill 治病 (to cure an illness), etc. are all commonly used phrases, where 疾病 is not used.
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