Both verbs mean not to accept something. The difference lays in the usage because to refuse to do something means to say that you will not do something or you do not accept something, a proposal, for example. In this case, you reject it, that is, you refuse to accept it. You can reject a person; in this case, you do not show interest in them, at all. To refuse refers to decline to accept something that was offered, for example, an award. In military sense, it means to curve back, to bend. A claim can be rejected but a permission or a request can be refused.
