McGrath: Oddly, no, usually, since it's not English, it's a transliteration from Hebrew/Yiddish. Pronounciation does.

But usually Abby is the same as Abbie or Avi with a short a and derives from and is the diminutive of Aba.

Aby or Abie is usually a long a and derives from Abrabam (the root of which is Aba, anyway, you'll notice.)

Means "father." As a kid, my daughter got to call me by my first name, therefore. She also got to introduce me as "This is my aba, Aba." She thought that was very funny.