Again, Darwinism says they ARE related. How closely is irrelevant. Animals adapt to their environment, but they don't change into other animals.
Vultures only give birth to other vultures. A Vulture will never give birth to a anything other than another vulture.
Do you have a mechanism to explain HOW an animal can adapt in “the same way to the same environment”? Would it be natural selection of genetic variation? Divine intervention? A lamarkian will to change? What?
How does an animal adapt to its environment?
And if you accept that old world and new world vultures adapted the same way to the same environment (losing neck feathers to better feast on carrion) - then obviously a non vulture bird population “adapted” into being a vulture population in response to the “environment” of being a carrion eater - two different times in two different locations (the old world and the new world) from two very different bird lineages.
And a non vulture bird need not give birth to a vulture bird in one generation, as one unlearned entirely in biology would conceive of it - no more than a speaker of Latin would give rise, in one generation, to an Italian speaker unable to converse with his or her parents.