Hi Bro

DHCP relay listens to local broadcast messages from PC, and forwards these messages on another network towards the DHCP server. The DHCP server responds, and the replies is then forwarded back to the PC.

DHCP proxy is a fully-functional DHCP server and client built inside. The PC establishes IP leases from the DHCP server on one interface, and then keeps these addresses in a pool. On another interface, the server side of the implementation provides leases to other machines using that pool.

Cisco PIX/ASA Firewalls supports both method. In many of my previous implementations, the FW interface on which it behaves as a DHCP server has a dedicated, manually-configured address pool, and the only thing the proxy feature does is get configuration parameters from another upstream server e.g. equipment configuration, as shown below;

Router(config)#boot ?
  bootstrap  Bootstrap image file
  config     Configuration file
  host       Router-specific config file
  network    Network-wide config file
  system     System image file

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