Being in a relationship is exclusive. As in not seeing anyone else but each other. Dating is more casual, and at times you both may be open to other options. Yet some see no difference. You should maybe ask your partner for clarification of how they perceive the situation so that you both are on the same page.
Dating is where you go out with several different people or even just that one person, and you just go out on dates, but being in a relationship, is where you commit to one person. And you say that is my boyfriend/girlfriend.
My opinion is when you date you just hang out talk and have fun with no strings attached. And relationship could mean something more seriouse something that isnt just friendship but love and being more close!(: