AMI of Hibernate Instance versus AMI of Shut Down Instance.

The differences between Hibernate and stop are as per the following documentation.
The major difference is whether the memory state is saved or not.
https://docs.aws.amazon.com/AWSEC2/latest/UserGuide/ec2-instance-lifecycle.html#lifecycle-differences

It is not recommended to take snapshots with Hibernate.
Basically, when creating a snapshot, it is better to take it while the system is stopped.
https://docs.aws.amazon.com/AWSEC2/latest/UserGuide/instance-hibernate-limitations.html

If you create a snapshot or AMI from an instance that is hibernated or has hibernation enabled, you might not be able to connect to a new instance that is launched from the AMI or from an AMI that was created from the snapshot.