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
The major difference is between the type of service referred to. A snapshot is of an EBS volume where you are able to save state and reboot with the same data at a certain point in time.
An AMI is similar, but its for the EC2 instances themselves. You cannot take a snapshot of a non ebs backed instance, but you can create a AMI (system image) of one.
Generally I use EBS snapshots as backup solutions for a database volume and I use an AMI to save instance configuration