What ARE birds?

Neither the European, American oro Japanese robins are birds. Not all members of the genus Petroica are birds.

Cats are not birds.
Four toed earless skinks are not birds.
Four toed elephant shrew and jerboas are birds!
Four toed hedgehogs are kind of birds? I'd feel bad calling it one way or another.

Not all dinosaurs are birds.
Komodo dragons are not birds.
Bearded dragons are birds!

Birds are not organisms which have had their taxonomic classifications changed.
I cannot ascertain if all fictional animals are birds or not, please provide examples.
Indominus rex does not appear to be a bird.

A hint: birdness is not predicated on scientific names. All species have a scientific name.
Boxfishes are birds!
Pyramid butterflyfish are birds.
Orbfishes, alternately called Round spadefishes, are not birds.