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The bay owls (Phodilus) are a genus of Old World barn-owls. The defining characteristics of bay owls are their smaller bodies, in comparison to other barn owls, and their U- or V-shaped faces.

 The name is from the Ancient Greek phos for "light" or "daylight" and deilos for "timid" or "cowardly".

1/ Oriental bay owl (Cú lợn rừng, Phodilus badius)

badius in Latin meaning reddish brown, chestnut colored, bay 

Tyto is a genus of birds consisting of true barn owls, grass owls and masked owls that collectively make up all the species within the subfamily Tytoninae of the barn owl family, Tytonidae.

1/ African grass owl (Cú lợn đồng cỏ châu Phi or Cú lợn lưng nâu, Tyto capensis)
2/ Barn owl (Cú lợn lưng xám, Tyto alba), also known as the common barn owl

3/ Eastern barn owl (Tyto javanica)

4/ Eastern grass owl (Tyto longimembris), also known as Chinese grass owl or Australasian grass owl
Some authorities consider this owl to be conspecific with the African grass owl, Tyto capensis, other consider it to be a valid species.

Strigiformes, Strigidae: from "Strix", a Latin word for owl (also the same in Greek).
Tyto: Greek tuto owl, night-owl.

Barn-owls (family Tytonidae) are one of the two families of owls, the other being the true owls or typical owls, Strigidae.

Strigiformes: All Owls are classified as members of this order. 
The name is formed from "Strig", the plural form of the Latin word "strix", meaning "owl", and "formes", meaning "forms".

Strigidae: The family for all Owls except Barn Owls, derived from "Strix", a Latin word for owl (also the same in Greek)

Tytonidae: All barn owls are members of this family. The name is derived from the Greek word "tuto", which means "owl".