`Amazon` named services are core building blocks (e.g. ec2 is just servers). `AWS` are services built on top of the `Amazon` services (e.g. Lambda runs on their EC2 machines, Batch runs on EC2 machines). usually
I don't believe that's the reasoning; and although I worked at AWS in the past I don't know for sure what's the reasoning behind choosing "Amazon" or "AWS" prefix for a service name.
For example, RDS is definitely a service built on top of other core services (EC2, S3, KMS, Route 53), its name is "Amazon RDS" and not "AWS RDS".