I know that "grandfather" is "Abuelo" in Spanish and that "grandmother" is "Abuela" in Spanish.
I heard a youngster refer to his grandfather as "Abue" (OB-way); I guess this is something like "gramps" or "grandpa." But in English we differentiate grandpa from grandma with "gramps/gram-pa" and "gram/gram-ma."
Is the nickname for grandmother the same in Spanish as it is for grandfather ("Abue")? If so, this is one of the rare occasions where English usage is more specific than Spanish.
It is. I have actually never heard much "abue" (I have heard "abu" more often), but it works as a "pet term" for both "Abuelo" and "Abuela".
There are several pet terms for abuelos and abuelas. Among many others:
Abuelos:
yayo, tata, abu, abue, nono, papito, papá + nombre del abuelo (eg. Papá Félix), agüelillo, agüelito, "abelo", lito, bueli.
Abuelas:
yaya, nana, nona, abue, güeli, abu, mamá + nombre de la abuela (eg. Mamá Consuelo), agüelilla, agüelita, "abela", lita, bueli.
There may be many other depending on cultural or regional differences or variations of Spanish dialects. There may be others, depending on what toddlers can pronounce or particularities of a family (like calling "abuela" to one of the grandmas and "yaya" to the other).
With some of these terms, without any context, you could not be sure about the gender of the mentioned person.