Question about avian sex chromosomes

[Dora Smith <villandra@austin.rr.com>]

I have an original nonscientist question.   But I did take two years of
biology in college.   Thought I knew the answer to this one.

As far as I know, all higher living things, let alone all higher animals,
that reproduce sexually, have a female with two X chromosomes, and a male
with one X chromosome and one Y chromosome.

I am repeatedly seeing authoritative sources on the genetics of budgie
(parakeet) color breeding, state that with budgies the male has two X
chromosomes and the female has just one X chromosome.   I got some even more
interesting story on what else she has but forgot the details.   Therefore,
my authoritative sources consistently continue, a female's color will
necessarily be determined by which of a certain color gene is on her one X
chromosome.

Do birds do sex chromosomes differently than mammals do?   If so, since
dinosaurs and mammals share common ancestors, how could such a thing have
happened?

Yours,
Dora Smith
Austin, Texas
villandra@austin.rr.com