This is a typical thing that our BM and my SD did with SGD.  We treated all 9 grandkids, no matter whether DH's or mine, exactly the same.  One time, SGD, then about 7, piped up with, "You're not my real geandma".  I said, that's right and changed the subject.  It was crystal clear to me that BM and SD had told her that.  It was true, i wasn't.

Flash forward, SGD is now 27, a teacher & now expecting 1st child.  She stays in contact with us and surprised us last year with kind Christmas gifts.  During SD's traumatic 10 months here, SD was driving us crazy one day, high on drugs.  DH called SGD for help.  She came and straightened out SD ("Go downstairs! You're scaring Grandma!")  I would just take it in stride and continue to treat the child the same.  Kids hear weird things about stepfamily but when they get older, they figure it out.

What does your mother think? What does she want to be called? Maybe your sd and your mother can come up with another name together if your sd does not like grandma and your mother agrees to trying something different. I would emphasise for your sd the importance of using the name that someone requests that you use as a sign of respect, but acknolwedge that if she really objects to the name grandma that her and your mother can discuss it together to work out what works best for the two of them. 

Your sd does have a different relationship to your mother than your son has with your mother and she has a different relationship with your mother than she does with her biological grandparents. Dismissing that is foolish. Acknolwedge it and work with her and your mom to find a solution. You may end up back at the starting point and sd agreeing that calling your mother grandma is ok for her after all or you may end up with the two of them having a different nickname. 

I'm with the kid on this one. If she doesn't call you mom then she shouldn't have to call your mother grandma.  Sounds like she is doing her best to find her place and navigate the tricky stepfamily world.  If I could whisper in sd's ear I'd let her in on the secret that having several grandmas blood related or not is a good thing!  Let her know that she's right and it's fine to respectfully call step grandma by her first name.  

I have two gskids, one call me grandma first name, the other just my first name.  I'm fine with either.  

Well - it's not her grandmother, just like you aren't her mother - so if she was being rude about it, vs. just exploring what's true, then the rudeness is what should be focused on, not the fact that she doesn't see her as her grandmother. 

If your mom isn't comfortable with her first name being used, she can be Mrs. Whoever.

My SD did the same to my parents, who had welcomed her with open arms, and treated her exactly the same as our bios. Same amount of photos around their house, same gift expendiature, same referral as being their grandkid. My mom in particular would take ots of time and interest to speak with SD, help her, show her love.

Until it all came to a big end. At the same time SD stole from us, had BM accuse us of child abuse amongst may other (untruthful) atrocities, and suddenly moved away without so much as a goodbye, my mom found out SD had been lying to her and using her. 

My parents disengaged. Took down all the photos of her, no gifts, no contact at all. Now it's been years of no contact to anyone in our family (aside from the occassional guilt trips and demands to DH, of course refusing to acknowledge me, our bios or extended family). They have finally moved on and saw hr for who she is.

I hope your mom doesn't take personal offense to your SD, and protects her own heart. Hopefully your SD, being young, will come to her senses and not be swayed by BM (as is likely culprit), but the signs are not good. Your mom sounds lovely. Maybe in your situation your DH could have a talk with SD and explain blood doesn't have to make a family, and extra people loving her and treating her well is always a good thing to have.