Nightshade is just a family. A bunch of plants that share genetic similarities.

We consider them different for the same reason that we consider cats different from dogs. Cats belong to the Felidae family (aka felines), and dogs belong to the Canis family (aka canines). Those families are used to describe the basic characteristics of all family members.

For plants, the Solanaceae family (aka nightshades) have different characteristics from the Brassicaceae family (aka Cruciferous veggies)

One of the characteristics of the Nightshade family is poison. You can avoid the poison if you are careful and eat the correct part... but some people avoid the whole family all together.