I have no doubt in my mind that most birds are smart Susie. For 18 years I was the papa of a Quaker Parakeet that I named Keebler. She passed away about gosh...four/five years ago. She was my little angel, and oh so very smart! She could sing the following song, to the tune of "I'm a litttle teapot" all the way through, and loved singing it with papa.
I'm a little quaker, green and stout,
Open up my cage and let me out,
Better pick me up or else I'll squawk
Rub my tummy and then I'll talk.
She understood things too. Once I was carrying the laundry though the kitchen to the laundry room, and dropped a towel on the way there. She told me, "whoops! You dropped something". The same thing I would tell her when she dropped a treat or toy.
Her vocabulary was immense. She knew "I Love You" and laughed when I laughed. And she knew how to call Chip, my dog, just like I did.. "Chip, come here". She imitated the dogs barking too. Oh geeze, and a whole ton of other things that I can't think of right now. I haven't had my coffee yet..hehehe!
I don't think the budgies are quite that smart, but we'll work on learning new things with them as long as they want to learn.