Bitto Rani & Choti Rani are the 2 nick names that Shanti devi uses to address her granddaughters.
While she has given them nick-names, I have also noticed that none of the others in the family use those names, only Shantidevi does. Be it Kausalya, Shivam, or Raghav, always address the girls with Nimmi or Preeti and not Bitto Rani / Choti Rani.
So, in a way, it is good that Shanti devi has some affection for her son's daughters and addresses them with nick names, the issue is - She is not consistent in the addressing.
From episode 1, I have seen that she calls either of the girls with either of the names. Since Nimmi is in more scenes than Preeti, I have seen Shanti address her as both 'Choti Rani' & 'Bitto Rani'!
At this point, I don't think it is the character, but the actor, Krutika Desai, who is messing it up. Krutika being a great actor, it is kinda weird that she is not consist in addressing these girls. In a rush to finish off the episodes probably no one from the production team is correcting her while shooting?
If anyone from the channel or the production/writing team is reading this, please take this feedback to Krutika and request her to be consistent with her nick names.
The names are nice though.