Hi. They are parrots native to my country Australia. They can be easily taught to talk by repeating the same words. In our outback they gather in flocks numbering hundreds to thousands drinking at waterholes.
Males are the easiest to teach to talk, perhaps you had a shy female or didn't persist enough.
Erroneously they say that the name Budgie is obscure and the origin not known.
That is false. I had a great Aboriginal friend and the name Budgie came from his peoples language. They were known as the little friendly bird. Often my Aboriginal friend would call me budge, friend.