This paper is devoted to studying controllability problems of linear stochastic control systems with controls only in the drift terms. It is well known that such a system is not exactly controllable. We first construct an example to show that it is also not approximately controllable under some natural condition. Next we introduce the notion of partial approximate controllability and reveal that it is equivalent to some weak unique continuation property of backward stochastic evolution equations. Then we prove that this kind of unique continuation property holds. Finally, two examples concerning controlled stochastic parabolic and stochastic Schrodinger equations are presented.