CCNP - ENTERPRISE - To 'Delete' or to 'Erase'?

When do you use the commands Delete or Erase?

Well it depends on what you are wanting to do.

If you want to remove a file, you use the delete cmd, for example:
R1#delete flash:config.old
or
SW1#delete vlan.dat

If you want to remove system information you use the erase cmd, for example:
R1#erase startup-config

If in doubt use the ? to inspect your options:
R1#?