We call grandmothers the same whether they're from the mother or the father side, but those different words represent different accents, I'll give you an example from my country:

As a Jordanian from a small town I call my grandmother (jeddity: جِدتي), but Jordanians from Palestinian origion they usually call their grandmothers (sitti: سِتي), Syrians and Lebanese usually call her (teta: تِيتا).

So it's really a matter of different accents :)

Thanks Mumtaz and Liwaa!!! All questions clear. شكرا جزلا!

جدة "Jaddah" is the Formal version of the word (Al-Fosha)

and it's used in many dialects (Egyptian - UAE - Saudi ...)

ستي "Sitty" has the same meaning but not formal, (used in Lebanon, Syria, Palestien ...)

the word is derivated from the word ست "sitt" which means Madam (+ باء المتكلم) so it means My Grandma
"Teta" is used in Lebanon and "Tete" in Syria (and I don't know about the others) the same dialects which use "Sitty", Teta/Tete is used by the chidren usually 

jaddah is in MSA, the other two are from another dialect. I know that tetah is used by Palestinian and some Syrians. Some Hejazis (west coast of Saudi Arabia) I know use sittah to refer to their grandmothers.

the word Jaddah is in classical Arabic ..

as for  the word ستة,firstly, it is not like this , and I'm sure you mean ستّي or ستّو and also you mean (تيتة)  in stead of  تتة .. and all of these words :  ستّو  and ستّي  and تيتة  means jaddati ( my grandma) , but in egyption dialect .