Bilinear systems,matrix systems and right-invariant systems are distinguished first.Then controllability theorems of such three different systems are summarized,the key points focus on the necessary and sufficient controllability conditions for right-invariant systems,and the relation with bilinear systems. Controllability theorems of these three different systems are especially emphasized by using Lie groups and Lie algebra. Different controllability theorems of quantum systems using similar method are analyzed in detail. Corresponding relations of controllability between quantum systems with bilinear systems are pointed out by means of comparison,and each type of controllability applied to different situations are also given.Relationships among different notions of controllability of quantum systems are established.