Even though the eating habits of each bird is completely different DNA testing shows they are within the same class of Ciconiiforme.
New World vultures had always been considered a raptor, grouped with Hawks, Falcons, etc. DNA tests came along and confused everything.
The Ciconiiforme class looks to be a wide group since Herons and Ibis are included.
Storks and vultures share the unusual characteristic of cooling down by urohydrosis—excreting urine on the legs to increase evaporation.
Store that fact away. The next time you are at a party in an awkward conversation just throw this in.