There are several major competing bird classifications in use, most of which we have as dwc archives. We (or our users) should decide which taxonomy GBIF should follow. Unfortunately not all bird names exist in one source, mostly because of the many changes incl recombinations happening in Aves.
The current Catalog of Life follows ITIS for all bird names within Aves:
The ITIS version we have has 33 accepted orders, 193 families and 9.924 species: http://www.gbif.org/species/107233360
"Our" CoL has 33 accepted orders, 225 families and 10.306 species:
Alternatively we have the Clemens checklist from Cornell:
with 34 orders, 234 families.
10,404 species, 20,768 subspecies
Or the IOC World Bird List from the International Ornithologists Union:
with 40 orders, 238 families.
10,567 extant species and 149 extinct species.
ITIS recognizes 40 bird orders:
Is there a clear main bird taxonomy out there that most birders follow?