aws vpc endpoints - how it works

Question

I am trying to understand the concept of how VPC endpoints work and I am not sure that I understand the AWS documentation. For example, I have a private S3 bucket and I have an EKS cluster. So if my bucket is private I believe that traffic from the EKS cluster to S3 does not go through the internet, but only through the AWS network. But in a case my s3 bucket was public, then probably I will need to set up the VPC endpoint, so traffic will not leave the AWS. The same logic I would expect with ECR, if it is private you load images to your EKS through the AWS network. So what is the exact case when you need to use the VPC endpoint within your AWS account (not from on-prem or another VPC)?