Static identity NAT is the static NAT configuration on ASA/PIX, and it's bidirectional. It is configured to statically translate to a static ip address.
Identify NAT is the nat 0 configuration (without ACL), which translate the real ip address to itself. However, identity NAT is unidirectional.
Here is further explaination on both with examples for your reference:
http://www.cisco.com/en/US/docs/security/asa/asa80/configuration/guide/cfgnat.html#wp1043425
Hope that helps.
