The migration guide from AWS Elasticsearch Service to Elasticsearch Service on Elastic Cloud outlines a detailed process for users looking to leverage advanced features and support provided by Elastic, which are not available from Amazon. It offers a step-by-step method to perform a "lift-and-shift" migration, starting with a snapshot of the AWS ES cluster stored in an S3 bucket, and then restoring it to an Elastic Cloud deployment. The guide emphasizes the necessity of programming skills and familiarity with AWS SDKs, especially in Python, to successfully complete the migration. Users must set up IAM roles and policies, create necessary AWS resources, and execute Python scripts for snapshotting and restoring. Additionally, the guide notes that Elastic Cloud offers a 14-day free trial, supports multiple cloud providers such as AWS, GCP, and Azure, and provides ongoing updates and unique features like Canvas, APM, and machine learning capabilities.