Tetras are members of the scientific family of Characidae (Characins). Barbs belong to the family Cyprinidae (Cyprinids). So they are different even if they sometimes look similar to an inexperienced eye. But as you said, they have 'whiskers' or barbels at either side of their mouths. It's their most common physical attribute that sets them apart from other mid-swimming species. So the barbels are what make them different... hence the common name 'barbs'.