Response is information about the status of the transaction (1,2 and 3). Use this response to integrate for Pass and Fail of a transaction. Response table is on page 48 of the Services API.
Coderesponse is the transaction status from the processor. These are NOT unique and a single status can have different meanings by processor. Appendix 3 list examples of coderesponses.
Status is GATEWAY status, this provides additional information about the transaction. For instance, if FBI Tools stopped a transaction, you would see that indicated here. See Status table on page 48.