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
You can think of an AMI as a generic template for a machine with OS and installed components being preserved.
A Snapshot can include everything an AMI does, but also saves the disk data of an EBS volume.
Which one you decide to use will generally be dictated by whether your instances are EBS backed and if you want to exactly recreate a machine with all data intact or just want a generic machine template.