The Vedic Religion is based on the three books of the Veda. All of the different chants, rites, and rituals, are followed by those who follow this religion. Hinduism is a religion based on the type of religion that was followed by the Indians and all other sub-continents during the medieval period.
Do take note that while they are similar to religion, it would be safe to say that it is the Vedic Religion that also molded Hinduism. It is likely that Hinduism will not be what it is today without the traditions that were followed by the Vedic religion. Details about the Vedic religion was gathered from some of the rites that are still being done in Hinduism right now and also some of the written text about the religion.