What is the difference between filesystem backup and a server image?
 

Does a server image include a filesystem backup, as well as OS settings?
Would someone confirm with me what exactly a server image is?

On a related note, what software is easiest to use for these two tasks, if they are different? Thanks.

Not sure this is the correct answer but:

A Filesystem backup is a storage of data held so individual/whole file/system restores can be performed.

A Server image is usually the image used to create a new server in the first instance and can't be used to restore user data.