The difference between the modes is that in Dictation mode, the default, any words you say that aren’t Voice Control commands are entered as text in the active text area. If there's no active text area, there's no real difference. The commands that are active under either mode is virtually identical. The primary way to tell if you're in Command mode is that a dark icon of a crossed-out character appears in the text input area to indicate you can't dictate. The icon normally appears about three seconds after the last interaction. Since both "Dictation mode" and "Command mode" commands are always active regardless of the current mode, you can always say the one you want to guarantee you're in the desired mode.
Command mode is handy when you're working in an area with conversations occurring nearby or you want to answer the phone at anytime without worrying it will end up in the currently active text area.