Natural and native are both from the same word source, which is the same source as having anything to to with birth, such as natal, nativity, national.
http://dictionary.reference.com/browse/native
Yes, they both pertain to birth.
Native pertains to the soil the birth took place on and Natural pertains to the persons who conceived the child aka parentage.
Thanks for clearing that up for us(sarc) even though we know you can't quite comprehend such a uniquely world wide held concept that has been the root of civilization from the beginning of man(Adam).