The answer might differ if you are asking about the common language, the way terms are applied in different ethnic, cultural, or social groups, or about the laws of inheritance in different jurisdictions.
Any reason why you might consider that they would not be legally considered grandchildren?
Having said that, that’s not to say that all grandparents are going to accept them as grandchildren, or give them equal standing as their natural born grandchildren, but that’s just the way some people are.
Edit: And to your subsequent question,they’d be step-grandchildren.
I favor the sociobiology and genealogy viewpoint so such things are all noted with qualifiers in my family when I describe relationships even though we have a bunch of every category from adopted to step-whatevers.
It is a personal and family preference regarding which one you use and none or right or wrong but some people may see it differently than you do. I personally regard the unqualified word ‘child’ or ‘grandchild’ to only mean your personal biological offspring and the biological offspring of your parents only but many people take offense at that.
However, I come from the Deep South where ‘Aunt’ and ‘Uncle’ can mean anything from the siblings of your parents or grandparents to older cousins or even close family friends that aren’t related to you at all.
There are no hard rules. You have to make them up as you see fit with the caveat that you cannot impose your own life choices on the way other family members or society in general see things.
I most certainly am like that and it is for practical as well as intellectual reasons. Don’t get me wrong, I like almost all of them and I like some of the steps and adopted ones better than my biological kin but there are clear legal and practical divisions dictating why not everyone can be just mixed in depending who who wants to marry or sleep with who or who decides they want an adopted foreign child at any particular time.
It doesn’t work that way. Biological bonds are permanent even if you can’t stand some of the people personally who you are stuck with. Almost all the rest are potentially transient and that is the big difference.
It’s only practical to make a distinction among your family if you actually, ya know, make differences between them in practice. My step-grandmother is, in practice, simply my grandma. My departed step-step-grandfather was simply my grandpa. They had both been divorced and widowed before meeting and had a bewildering variety of bio kids, step-kids, and step-step kids. Neither of them ever made any distinction between any of us in treatment, so what on earth would have been the point in making a distinction between us in naming?
If you adopt a child, are you their mother/father?
If you shack up with a gal and she has a kid, are you the daddy?
i would suggest that the defining “grandma/grandpa” role is set by the adoptive/nonadoptive child’s role with the (non)parent.
If you want to criticize your child’s choice of how ***they ***define their family relationship, by all means insist “I don’t care, that’s not my grandson!”
Of course, I don’t expect the new grandparents to have a nice warm “milk and cookies” moment if the brand new grandson is 20 years old and away at college when his proto-parents shack up. There is s slightly more reserved protocol for (near)adults that join a family. I also would not be surprised if grandparents dote more on their own flesh-and-blood; but outright rejection of a child - “you’re not my grandchild” - seems a bit harsh and cruel.