Brachiopod
Taxonomical history

"Traditional" classification
Inarticulata
Inarticulata
Inarticulata
Articulata
Articulata
"Calciata" approach
Lingulata
Lingulata
Calciata
Calciata
Calciata
Three-part approach
Linguliformea
Linguliformea
Craniformea
Rhynchonelliformea
Rhynchonelliformea
Orders
Lingulida
Discinida
Craniida
Terebratulida
Rhynchonellida
Hinge
No teeth
No teeth
No teeth
Teeth and sockets
Teeth and sockets
Anus
On front of body, at end of U-shaped gut
On front of body, at end of U-shaped gut
On front of body, at end of U-shaped gut
None
None
Pedicle
Contains coelom with muscles running through
Contains coelom with muscles running through
No pedicle
No coelom, muscles where joins body
No coelom, muscles where joins body
Pedicle
Long, burrows
Short, attached to hard surfaces
None, cemented to surface
Short, attached to hard surfaces
Short, attached to hard surfaces
Periostracum
Glycosaminoglycans and chitin
Glycosaminoglycans and chitin
Chitin
Proteins
Proteins
Primary (middle) mineralized layer of shell
Glycosaminoglycans and apatite (calcium phosphate)
Glycosaminoglycans and apatite (calcium phosphate)
Calcite (a form of calcium carbonate)
Calcite (a form of calcium carbonate)
Calcite (a form of calcium carbonate)
Inner mineralized layer of shell
Collagen and other proteins, chitinophosphate and apatite (calcium phosphate)
Collagen and other proteins, chitinophosphate and apatite (calcium phosphate)
Calcite
Proteins and calcite
Proteins and calcite
Chaetae around opening of shells
Yes
Yes
-
-
-
Coelom fully divided
Yes
Yes
No
Yes
Yes

Question: How are the Lingulida and Discinida grouped? 
Answer: In Brachiopod, the Lingulida and Discinida are grouped as Linguliformea, and the Rhynchonellida and Terebratulida as Rhynchonelliformea.