With regard to step-grandchildren, I think that people do tend to take into account whether or not they will also be inheriting from biological grandparents as well as the relationship they have with them.
I made sure that my step-grandchild got her inheritance from my late husband, but she won't be getting any extra from me. I did always make sure that she had birthday presents, Christmas presents and so on, plus I opened a bank account for her when she was a baby and placed what was then a significant amount of money (for someone on my income) in the account before signing control of it over to her mother.
She'll inherit from my husband's ex and from her father's side of the family. I was never allowed to have a close relationship with her. [Insert the obligatory "I wasn't the OW.] For whatever reason, she was encouraged to treat the ex's three partners as grandparents, but that wasn't allowed in my case. (I think the ex had made it clear that she wouldn't be happy about it.)
Not the grandchild's fault, but she's an adult now and - to be honest - it would have helped had she attended my husband's memorial service in person.
By contrast, my BIL's children were supportive and have made sure that their child at least know who I am, so I'm more inclined to give to them (as well as to my cousins' grandchildren).
I do feel that I'm being mean, but the following has stuck in my mind.
When the ex's affair partner died, he left everything to the ex. Quite understandable, I thought.
The grandchild's parents had a meal out with us shortly afterwards and then came back to ours for a few drinks. After a few drinks, the grandchild's father began to complain to me that no money had been left to the grandchild.
I commented that it was quite normal for the money to be left to a partner alone and that eventually it would trickle down to the grandchild.
The father then said, "Yes, but he should have left something to [the grandchild] because she called him 'Grandad.'"
I remember thinking "Oh. You'll not expect me to leave her anything then."