You are making the logical error of assuming that because your notation can not express a difference that there is no difference. There are two unstated assumptions that you appear to make.
All communication is two way and continuous.
All powers can be described as the ability to send or receive a message. The first assumption is the less problematical one. Depending on how it is violated it can result in a great number of different cases which may or may not be describable in terms of capabilities, but it does not change the results of the question you pose. The other assumption is more important. Consider the following scenario.