Fact: that difference is still maintained even if you accept the actual legal definition of "natural born citizen" as "citizen at birth".
I have always considered myself and my brother as a ‘citizen’ at birth by being born in the USA. We even went to war in WWII as ‘citizens’ in which my brother was killed on Okinawa. However, I never considered myself or my brother as ‘natural born(USA) citizens’ because our parents as immigrants were not naturalized citizens. I have no problem with recognizing the unique attribute of ‘natural born’ citizen not applying to either my brother or myself even though as a second grader I had thoughts of being POTUSA.