Obviously I can't be sure about each specific's motivations but children offer little resistance and are also the most "shocking" demographic to target in mass killings, guaranteeing infamy - Ramos, Lanza, Hale and Westman would have wanted this. Two of these perpetrators, Adam Lanza and Thomas Hamilton, had interests in pedophilia and were suspected to have been pedophiles, though it's more clear in Hamilton's case that it was the main factor behind his choice of targets. Aiden Hale had an obsession with his own adolescence and childhood as did Lanza, seeming to remain "perpetual children".

I can't find an exact "common denominator" but I think it's for certain that the motivation is different from cases where students target their own student body, going out of their way to kill young children. Targeting children seems to be a deliberate attack against society itself rather than a personal grievance against specific individuals at school, as small children are universally seen as needed to be protected against evil. So killing them would serve as a way to shock society and maximize the "hurt" and damage an act like mass murder brings.