At a minimum, an EC2 instance will have an EBS volume for the operating system. You can add additional volumes.
What's the nature of the data on the EBS volume(s)? When dealing w/ transitory instances like spot instances or scaling groups, data on EBS volumes tends to be transitory.... though you could reattach retained EBS volumes to new instances.
If it has to survive terminated instances & be reused by new instances, S3 might be a better fit than EBS (unless you need higher performance available w/ EBS SSD types).
AMIs are templates of an EC2 instance & it's associated EBS volumes. Snapshots associated w/ an AMI are backups of the EBS volumes allowing you to return to the state at the time the AMI was created.
RE. Stopping vs terminating: With termination, you can (but don't have to) delete the EBS volumes to save money. If you stop, you are just pausing. You could delete volumes (except the system volume where the OS lives, of course) depending on having a snapshot to recreate, ability to lose data and/or fix paths, etc.