So I am having trouble working out what, specifically is the difference between these two.
As I understand it, a snapshot is simply a backup of the disk drive, where
I was confused by that as well. Here's simplest way of understanding it:
EBS Snapshot very often represents a backup of specific EBS volume, it might be any volume (Root volume, data volume, etc.)
AMI (Amazon Machine Image) is a backup of Entire EC2 instance. For example, with proper configuration it's possible to create AMI which includes multiple EBS volumes.
Now, it might sound confusing, but they are both stored as a "EBS Snapshots".
Just think of that way:
EBS Snapshot is a just a data backup.AMI is a representation of system state at specific time. You can also boot from it.