Here is another cover with both species already discussed. This complete set, issued by Russia in 2014, is a joint issue with North Korea. The stamp to the left shows the osprey (Pandion haliaetus) while the one to the right the Eurasian sparrowhawk (Accipiter nisus).

Thank you Elena!

In 2021 Croatia issued a set of two stamps featuring the white-winged woodpecker (Dendrocopos leucopterus) and the middle spotted woodpecker (Dendrocoptes medius). The first species can be found in Asia while the second one primarily in Europe.

The stamp set is a joint issue with Kyrgyzstan.

This set was issued in 2009 and it is a joint issue with Bulgaria.
Eurasian Woodcock (Scolopax rusticola): It can be found in temperate and subarctic Eurasia. Its main food is earthworms but its diet also includes insects and their larvae, seeds and freshwater molluscs. It is a game bird.
Rufous-tailed Rock Thrush (Monticola saxatilis): It can be found from southern Europe to central Asia to northern China. In winter it migrates south of the Sahara. It feeds on berries, insects and small reptiles.

Here is another cover from USA badly postmarked. The bird stamps from left to right were issued in 1969, 1971, and 1994. The last two were a joint issue with China. We already talked about California Condor so I will focus on the other three stamps.
Northern Flicker (Colaptes auratus): It is a member of the woodpecker family. This migratory bird lives in North and Central America in woodlands. It has three subspecies of which one is unfortunately extinct. It feeds on insects, fruit, berries, nuts and seeds.

Whooping Crane (Grus americana): It lives in North America and it is an endangered species. They feed on crustaceans, mollusks, aquatic insects, fish, frogs, snails, small rodents, berries etc.

Black-Necked Crane (Grus nigricollis): It lives in Asia and it is an endangered species. Like all cranes, they are too omnivorous.

Another joint issue this time between Iran (cover) and Portugal (stamps) in 2009.

White-tailed Eagle (Haliaeetus albicilla): It is also known as Sea Eagle. This bird of prey can be found in northern Asia and northern Europe. Apart from other birds and small mammals it can also eat fish. With the reduce of food sources and the poisoning by farmers, the Sea Eagle has become an endangered species.

Osprey (Pandion haliaetus): It is a fish-eating bird of prey and it has four subspecies. It has a worldwide distribution and it is a migratory bird.

Here is one of my Chinese covers, thank you CJ. The set was issued in 1997 and it is a joint issue with Sweden.

Lady Amherst's Pheasant (Chrysolophus amherstiae): It is native to south western China and Myanmar. Only the male has such a colorful plumage. A small population has been introduced to England. It feeds on grains, leaves and invertebrates. At night it roosts at trees.

Ring-necked Pheasant ( Phasianus colchicus): Ring-necked pheasant is the name for subspecies of the Common Pheasant, a game bird native to Russia. This subspecies have been introduced as game birds in many parts of the world. There are about 30 subspecies. they prefer to live in grasslands near water and they eat fruit, leaves, invertebrates, seeds, snakes, birds, small mammals and lizards.