My question can be elaborated as follows: When graduate students work together on a research project, are they usually expected to work on the same exact things, at the same exact time, or would it be more reasonable to have a division of labor and divide the work load?
It's really like any other collaboration. Presumably the (student) researchers are working together because they have a common interest in a problem and possibly have some complementary expertise that's useful for solving the problem. So they'll interact and as the situation merits it will divide up tasks (or work on some aspects together). There really isn't a single rule for this.