Yes Noida and gretaer noida are two different cities ,both are governed by different authorities i.e noida ny noida authority and greater noida by greater noida authority since the area is very large and and it require large development in coming time so needs to be diversify ...
As far as I know both the cities come under Delhi-NCR. May be there is some legal issues between the two cities for which the RWA's doesnot want to come under one roof.