Persistence of local SSDs of EC2 instances

Solution 1:

Your test was valuable, confirming such disks only live until the instance is stopped.

Yes, this is instance store. AWS writes a lot of marketing copy for each instance type, and sometimes reaches for synonyms. "Local" and "NVMe" emphasizes low latency. "Physically connected" or "coupled" is restating that these cannot be attached to another instance. "Coupled to the lifetime of the instance" is a polite way of saying they will be deleted on stop.

EBS also exists, persistent disks with more features. Local SSDs do not need to be anything other than scratch space, when fast SAN storage is available.