First things first, it depends on which Magento edition are we talking about:
- If we consider hosting Magento Open Source in AWS, then you have only the functionalities provided by the Open Source edition, you don't pay any Magento license + you have to make your own AWS infrastructure architecture design by yourself (which services to be installed, versions, resources to allocate for each, tools to be installed, configurations to be made) and tell Amazon which are your needs and pay the AWS services.
- If you consider Magento Commerce on AWS, then you will have to pay the Magento Commerce licence (for all the Commerce functionalities you don't have in Open Source) + build your own infra architecture design by yourself and tell Amazon which are your needs and pay the AWS services.
- In the context of Magento Commerce Cloud, we are talking about having to pay a Magento license that includes all of the Magento Commerce features, plus extra tools like Business Intelligence or Paypal Onboarding Tool + an already configured infrastructure architecture with the environments, CDN, New Relic monitoring, CI/CD, high availability (for Pro plan), support, etc. Also, on the Pro plan, you can choose which IaaS to be used (AWS or Azure). Here is an overview of this automated hosting platform.
Please check the Magento Commerce Cloud architecture for details about the different Magento Cloud plans.