Parent Dc & Child DC have the same schema or child shared some part of the Parent Dc .?

There can be only one Schema master in the Forest, and it is the responsibility of the DC holding the schema master to replicate the changes in multiple copies of schema in all of its child domains in trees.

There can be very low or almost nill chance of having inconsistencies in schema of child domains, If you still want to know the difference you must register the schemamgmt.dll and then load the schema management console and check what are the differences.

Only one schema per forest and they share the same schema .