I don't it's an issue of different understanding or even any disagreement.
I simply think that Pres Nelson, Oaks, Bednar, and possibly others take a more legalistic and literal approach. The "Mormon" usage is just one example.
Elder Uchtdorf and others are the more gentle, subjective gospel teachers. Nothing wrong with that and this is evidenced by member comments & response to both groups.
I simply don't see Oaks selecting counselors that don't match his perspective.
I still think Eyring & Bednar unless Pres Eyring age/health play a factor.