common “普通的,一般的”侧重常见的常有的,人人皆知的,如：Apples are very common in North China.苹果在华北很常见.也可指“平凡的等”,如 the common people 平民.

normal “正常的,标准的,普通的” 侧重与常规,标准等一致,如 the normal temperature of the human body.人的正常体温The baby's weight is normal.