This is not about parrots but about songbirds like canaries, finches, etc. [I know that tiel people say that their cockatiels 'sing' but they don't, they just vocalize] but I thought this article would still be interesting to you because there are species of parrots where the vocalizations of the males is different from the females (like cockatiels and budgies, for example].
https://www.sciencedaily.com/releases/2 ... 091840.htm