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Ciconia is a genus of birds in the stork family Ciconiidae. The genus name is the Latin word for "stork".
English common names for this species include the white-necked stork, white-headed stork, bishop stork and parson-bird. 

1/ Asian woolly-necked stork or Asian woollyneck (Hạc cổ trắng, Ciconia episcopus)
The specific epithet episcopus is Latin for "bishop".
Recently, the African and Asian populations are considered to be two different species: the African woolly-necked stork and the Asian woolly-necked stork. This is based purely on geographical isolation,yet there is no morphological or phylogenetic evidence yet to support this split.

2/ Black stork (Hạc đen, Ciconia nigra)
Ciconia nigra is from the Latin words for "stork" and "black" respectively.

3/ White stork (Hạc trắng, Ciconia ciconia) 

Storks are large, long-legged, long-necked wading birds with long, stout bills belonging to the family called Ciconiidae, and make up the order Ciconiiformes.

Ciconiidae, Ciconia: the Latin word for "stork".

The name Anastomus is from the Ancient Greek anastomoō meaning "to furnish with a mouth" or "with mouth wide-opened".
The mandibles of these birds do not meet except at the tip, or there is a gap between the arched upper mandible and recurved lower mandible.

1/ Asian openbill or Asian openbill stork (Cò nhạn, Cò ốc, Anastomus oscitans)
The specific epithet oscitans is the Latin word for "yawning".

Leptoptilos is a genus of large tropical storks, commonly known as adjutants. The genus name means thin (lepto) feather (ptilos). 

1/ Lesser adjutant (Già đẩy Java, Leptoptilos javanicus)
2/ Greater adjutant (Già đẩy lớn, Leptoptilos dubius)

Ephippiorhynchus is a small genus of storks. The genus name Ephippiorhynchus is derived from Ancient Greek ephippos, a saddle (literally something a horse back"), and rhynchus, "bill" (refering to the frontal shield).

1/ Black-necked stork (Cò Á Châu, Ephippiorhynchus asiaticus) 

Mycteria is a genus of large tropical storks with representatives in the Americas, east Africa and southern and southeastern Asia.
The genus name is from the Ancient Greek muktr meaning "snout" or "nose".

1/ Painted stork (Cò lạo Ấn Độ, Giang sen, Mycteria leucocephala) 

2/ Milky stork (Cò lạo xám, Mycteria cinerea)