What is the AWS equivalent of Azure Management Groups?
There is no direct equivalent to Management Groups in AWS.
You can achieve some of the same functionality by using AWS Control Tower, specifically around access controls.  I.e. you can set up groups and assign roles to any accounts in an AWS Organization on a per-account or per-group basis and have them deployed to child AWS accounts.
However, there is no such equivalent around, for example, resource allocation.
You can achieve some of the same functionality by using CloudFormation, or by using CT IAM policies policies with specific restrictions, but it's a much more convoluted process than with Azure.