I think you are making a mistake in thinking these groups can be so easily categorised. Hinduism is very syncretistic and to attempt to put rigid categories on different groups just ends up in an incredibly complex jumble. Don't forget that these groups were continually splitting and reforming but in most cases they used the "if they're not against us they're with us" method of determining relationships and not the more usual European religious method "if they're not with us they're againt us".