There are different kinds of backups, the following lists some of them:
Full backup means backing up everything.
Incremental backup means backing up everything that has changed since last full backup.
Differential seems to be another name for incremental.
Network backup usually means backing up a client to a backup server, this means the client sends the files to the server and the server writes them to backup medium.
Dump backups are not ordinary file by file backups. The whole disk partition or file system is "dumped" to the backup medium as is. This means it is also necessary to restore the whole partition or file system at one go. The dump backup may be a disk image, which means it must be restored to a similar disk with same disk geometry and bad blocks in same places. Watch out for this.
Level 0 -- 9Backup
Level 0 to 9 backups are a finer grained version of incremental backups. Level N backup means backing up everything that has changed since a same or lower lever backup.
Check the backup can be restored, with original file owners, permissions and timestamps.
To be useful, you must be able to restore the backup. Very often not only the contents of file are important, but their time stamps, permissions and owners. Check that you can restore the backup so that all these are preserved.