Species names
A bird species is not always and forever a bird species. Scientists gather new information - and now and then one species becomes two species or two species are lumped to become one species. Scientists disagree on lumpings and splittings. As a result, lists of bird species may consist of from 9200 to 10100 species of birds in the world. Another consequence of new information is that the zoological, latin, name of a bird changes when the bird is considered to belong to another genus than before. Another exciting thing, not so much of consequence for birds on stamps, is the discovery of birds new to science.

There are three major world lists available. The three lists are:

Sibley and Monroe, based upon the books
Sibley and Monroe, 1990, Distribution and Taxonomy of Birds of the World.
Sibley and Monroe, 1993, A Supplement to Distribution and Taxonomy of Birds of the World.
Sibley and Monroe, 1993, A World Checklist of Birds.

Dickinson, E.C. (Editor) 2003. The Howard and Moore Complete Checklist of the Birds of the World, 3rd Edition.

The Clements Checklist of Birds of the World, 6th edition, 2007.

Families and systematic order
There is no such thing as the world listing of bird species. Therefore I think the best thing to do is to choose the listing you feel most comfortable with. As a matter of fact, I feel most comfortable with world lists like the one by Clements.

Lists differ greatly on number and sequence of families. The Howard and Moore list is very much a traditional list. So is also the Clements list. The Sibley and Monroe list was the first based on DNA research. Families are fewer and re-arranged.