Gaillardia can be divided. There are about 30 different species of annuals and perennials.

Rudbeckia and Coreopsis are in the same family - Asteraceae. So they are related!

The problem with using "common names" for plants is that common names are different throughout the country. That's why using the botanical name is less confusing. But not everyone knows the botanical name. I try to use both when describing a plant.

Rudbeckia has several different common names: Black eyed susan, orange coneflower, and cutleaf coneflower. One of it's true botantical names is Rudbeckia hirta which is the the black-eyed susan, the most common Rudbeckia. There are several cultivars of this particular species: Irish Eyes, Marmalade, Becky Mixed.

Coreopsis has a large species of over 80 different annuals and perennials. The common name is Tickseed or Coreopsis.

Echinacea purpurea is purple coneflower. It used to be called Rudbeckia purpurea but the name was changed at one of the Horticulture Congresses where they change the Genus of plants. That could account for the confusion. They are closely related to the Rudbeckias.