Difference between Label and erase in netbackup

Have you tried the explanations in NetBackup Administrator's Guide, Volume I  ?

Table 8-14 Types of erase

SCSI long erase:
Rewinds the media and the data is overwritten with a known data pattern. A SCSI long erase is also called a secure erase because it erases the recorded data completely.
Note: A long erase is a time-consuming operation and can take as long as two hours to three hours. For example, it takes about 45 minutes to erase a 4-mm tape on a standalone drive

SCSI quick erase:
Rewinds the media and an erase gap is recorded on the media. The format of this gap is drive dependent. It can be an end-of-data (EOD) mark or a recorded pattern that the drive does not recognize as data.
Some drives do not support a quick erase (such as QUANTUM DLT7000). For the drives that do not support a quick erase, the new tape header that is written acts as an application-specific quick erase.

About labeling NetBackup volumes
When NetBackup labels a volume, it writes a record on the magnetic tape of the volume; the record (or label) includes the NetBackup media ID.
Normally, NetBackup controls the labeling of its volumes. In most cases, NetBackup labels a volume the first time it is used for a backup.
The volume label depends on whether or not the media has a bar code, as follows: 
■ If the robot supports bar codes and the media has bar codes, NetBackup uses the last six characters of the bar code for the media ID.
To change this default action, specify and select specific characters by using
Media ID generation rules.
See “Configuring media ID generation rules” on page 442.
■ For volumes without bar codes, by default NetBackup uses a prefix of the letter
A when it assigns a media ID to a volume (for example, A00001).
To change the default prefix, use the MEDIA_ID_PREFIX configuration option in
the vm.conf file.

Normally not needed to do ANY of these.
NBU will automatically write the volume label first time a tape is used for backup.

Media can be erased when you want to get rid of old media to ensure data cannot be read by anyone.

Manual labeling is needed when you use standalone tape drives and for some VTLs to reclame space.