Full: Full backup means backing up everything.
Incremental: Incremental backup means backing up everything that has
changed since last full backup.
Differential: Differential seems to be another name for incremental.
Network: 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: 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.
Level 0 -- 9: 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.