The object of meditation

I have been focused on the breath in meditation and I am interested in Vipassana, but I am confused about the object of meditation. I have read that you focus on the breath and as thoughts arise, you should observe them and then return to the breath and that it is the returning to the breath that increases one's mindfulness. I have also read that in Vipassana meditation, one shifts the object of meditation to the thoughts that arise and make them the object of mediation. This approach seems to be just sitting and letting your thoughts wander. Do I misunderstand the meaning of making arising thoughts the object of meditation? As it is now, I continue to make the breath the object and observe my other thoughts but generally do not pursue them, rather just categorizing the thought (like "planning the future" or "reliving the past") and then return to the breath.