Like many bird names, cadrinals do not form a monophyletic group.
They are not even all in the same family including the typical cardinals in the genus Cardinalis (Cardinalidae) and the red-headed cardinals in the genus Paroaria (Thraupidae).
It is ambiguity all the way down - Thanks DNA.

Species on page - 2 species in 2 genera in 2 families

Northern Cardinal (Cardinalis cardinalis)

Red-crested cardinal (Paroaria coronata)

Cardinalidae species on other pages (4 species in 2 genera) -

Painted bunting Passerina ciris

Lazuli bunting (Passerina amoena)

Blue grosbeak (Passerina caerulea)

Black-headed grosbeak (Pheucticus melanocephalus)

Northern Cardinal (Cardinalis cardinalis)

Northern Cardinal (Cardinalis cardinalis)
Family: Cardinalidae (cardinals)
Lone Pine Key, The Everglades, Florida
April 20, 2021
Canon R5

Northern Cardinal (Cardinalis cardinalis)
Family: Cardinalidae (cardinals)
Lone Pine Key, The Everglades, Florida
April 20, 2021
Canon R5

Newman

Northern Cardinal (Cardinalis cardinalis)
Family: Cardinalidae (cardinals)
Crown Plaza Ravinia
Atlanta
April 23, 2015

Sign

Northern Cardinal (Cardinalis cardinalis)
Family: Cardinalidae (cardinals)
Crown Plaza Ravinia
Atlanta
April 23, 2015

Cardinal close

Northern Cardinal (Cardinalis cardinalis)
Family: Cardinalidae (cardinals)
Central Park, New York
December 27, 2017
Canon 7Dmark2

Cardinal

Northern Cardinal (Cardinalis cardinalis)
Family: Cardinalidae (cardinals)
Central Park, New York
December 27, 2017
Canon 7Dmark2

Red-crested cardinal (Paroaria coronata)

Cardinal

Red-crested cardinal (Paroaria coronata)
Family: Thraupidae
Lima, Peru
July 16, 2017
Canon 7Dmark2