ANSWER: With Cloud services like AWS, you are paying for utilization. So with a system configured to take advantage of this during down time, you are only paying for storage during down time (ESB, S3 etc.)
and, if you don’t have an Egress waiver (for exporting data back out), a network fee for exported data.
More here: https://aws.amazon.com/blogs/publicsector/aws-offers-data-egress-discount-to-researchers/
– For a typical multi-user setup on AWS - an always on login/headnode and a spot-base “compute-fleet” with auto-scaling for compute nodes, most of the saving (if any) comes from the spot fleet - where you can set a maximum price per as a bid and they turn themselves off at the end of a job (or job set)
A word of caution - this is the AWS defined Stopped state of the instance, and while it is often tied to OS functions, the cost is tied to the instance (VM) occupancy and not activity, so if a user hibernate or suspend function is called to enter a low power state, you are still occupying the EC2 instance and will be billed for it.