Hi Nishant,
as you said, these are six competing constraints so it is normal that one constraint (budget) will be impacted by a change in another constraint (Resources).
however, one is not a subset of another. these are different constraints:
Budget: Contains the cost of resources and any other required tools, equipment, software, travel cost,...
Resources: has other aspects like skills of resources, availability of resources (both human resources and other like meeting rooms or any other equipment)