@jarmod's answer provides a good overview of the terminology. I don't think it addresses your visibility problem.
Your assumptions appears to be that the master account of the organization should be able to directly see all resources of all accounts within the organization in its AWS console or via the API. That's not correct.
The resources in the accounts are generally still separated (allthough some things can be shared, but that's another matter), but you can change into these accounts by assuming a role in the accounts and then you're able to see the resources - this is what @jarmod is describing. After you changed into the accounts, you'll be able to see all resources within that respective account.
To learn more about organizations and their capabilities, here are some helpful links:
Resources within an AWS Account logically belong to that account and not to its organization.