Yes, I would agree that each job has different responsibilities, tasks, and expectations.
As a story artist, I am expected to do many rough sketches and drawings for film/animation/cinematics and work with a director and other story artists to visualize scripts and sequences. It's a lot of drawing and key framed animation, but mostly rough as our focus is to do 'dirty work' before a film is animated or shot (it's just easier for the director this way and saves time if we already know how a sequence will be laid out).
As a concept artist, your focus is visual development of characters, environments, and props. So your daily regiment would include iterations of the same character/prop/environment until one is agreed upon, then a set of color variations, and then a final paint over. Of course, this is all subject to change according to the project's needs and art director's decisions. But, unlike story, you are only working on one item at a time versus a sequence of events (at least this is how I do it).
So, you can see how varied and specific each job can be. The big question is...what do YOU want to be? If you're not sure, drawing what you like and/or going to school and working on different projects can expose you to different types of jobs in the creative field. There is no right or wrong answer, it just has to be right for you :)