I was lucky enough to have 2 granny's and a great granny until I was about 8.
They were
Mums mum - granny nickname only used by grandchildren my fault as I'm eldest and couldn't pronounce her first name. The nickname is a reference to something she cooked that I loved but it's even a (not very nice) nickname for that, so that was shortened too and would make no sense to ANYBODY but our family. (We seem to have form for doing mad things like this. One relative is currently searching the family tree and a big obstacle has been deciphering nicknames that seemed to indicate certain forenames which the people concerned didn't have! Bloody confusing! I've mentioned on here before - in addition NONE of my male relatives (and a good few of the females too) go/went by their actual first name! They go by middle names or nicknames like Jack for James? That don't make sense? I was in my 20's before I knew most of their correct first names I was so used to the names they go by - clearly we're fugitives or spies or something 😂 d'oh moment - just remembered I'm guilty of this too, I go by my middle name not my first name 
it caused some confusion when I first joined Facebook as people I knew from school know me by my actual first name plus I changed to ex's surname 
so if anyone tried to google any of us they're screwed 😂😂)
Dads mum - granny nickname shortening of first name
Mums gran (her dads mum) - granny nickname based on physical characteristic only used by grandchildren and great grandchildren
Grandfathers were
Dads dad - granda big first name
Mums dad - granda wee first name
they had the same name which couldn't be shortened, one was much taller than the other but the "wee" one wasn't really wee and when his workmates found out that was our name for him he didn't hear the end of it for ages (oops sorry granda)
Weird family 😂
Scots (weegies originally) of Irish descent.
"Susan" 😂
But as an army brat I've lived all over U.K. And have friends from all over and I think it's more generational, my generation use gran/granny dds seem to use grandma or nan/nana/nannie and of course the women being referred to were/are of different generations too and may have chosen different pronouns because to them "granny" is old and they don't want to seem old?
That's why my mum & ex mil didn't want granny, they're both grandma "first name"
Ditto the men - my dads granpa and ex fil is pops
For info ex in-laws are Lancashire born and bred.
"Granny, Scotland. If I'd ever called her Nanny she would have buried me." 😂 I can SO relate!
LOVE the non British ones, I have a fair few friends and family who've emigrated/are expats and married locals in their chosen countries so their children of course have a wonderful wide variety of names and as those children became old enough to use Facebook I often noticed these relatives referenced in posts on their parents pages.
So there's oma's, nonna's, abuela's, mimi's...all sorts
Re greetings cards if you think finding granny is hard, try finding granda, granpa or pops!
"I'm from Glasgow and have a lot of cousins from both sides" me too how many? I'm the eldest of 17 cousins altogether.