Some thoughts about how the loveless siblings have different views on family/familial relationships, and how Void specifically approaches relationships in general by extension.
Clover sees some inherent connection in family. They are quick to latch onto FriendProgram, especially when they find out they're related.
They're also excited to share similarities with FP. The similarity in this particular example being that Clover has come to terms with being loveless, which they were in denial about. But knowing that it's something they share with FP and Void helped them against that.
And despite not being on great terms with FP and there not being much of an impression of their relationship with Void, they're eager to get an opportunity to bond with the both of them.
FP uses the label of family as a very neutral and objective descriptor. They have family because they are technologically related to other programs, but that's about it.
Several times throughout the game we see them refer to having family (outside of just Void) but there comes no inherent positive connection with that. FP is on good terms with Void but this clearly has nothing to do with their family relation, but the fact that the both of them tried to support one another.
Void, on the contrary, straight up doesn't acknowledge having any family outside of FP in the main game.
To them, family isn't a neutral descriptor, nor do they see inherent connection in technological relation. "Family" is a convenient label to apply to programs they get along with who also happen to be related to them.
I think in general Void likes to use convenient labels to describe their relationships with programs they are on good terms with. They presumably know that there are programs who don't want friendship through Vents and FP, but (before fully knowing who FP is) they quickly latch onto them as a potential friend, and later best friend.
And they also (if hesitantly) express that they view Half and Sparks as their friends, even if they're not sure it's reciprocated, and closely tie the idea of being their friend with having a positive connection with them.
I think Void being quick to call someone who just gives them consideration their friend while simultaneously hesitating to call most programs they know their friends definitly has to do with both the way the labs value friendships (and devalue less conventional relationships), and also with how Void has been conditioned to believe that they can't live up to being worthy of this type of relationship.
This doesn't mean they're not still valid in desiring friendships though, and I can imagine them post main game still using the term friend somewhat loosely and having a tendency for labelling their positive relationships, but I also like the potential development I'm reading into here of e.g. Off and Vents being programs who aren't family and would never describe their relationship to Void as friendship, but undoubtedly still value them.