Air carrier Captain reported being notified by ATC of going off course. The flight crew was flying towards the wrong fix; RADDS; and should have been flying direct to RAPZZ. The two fixes were similar in name and on the same route.

Narrative

After leaving out of our departure airport we were given direct to VIYAP. After that; at some point we were cleared direct to another fix. Whatever the actual fix name was; I did not immediately see it in our flight plan. I paused; did not reply to ATC as I was looking; and I may have told them to standby at some point. Just as they repeated fix name; I found it in the flight plan. They began spelling it out and I told them we finally had found it. They replied; yes it's a ways down the line. I then said we are now direct to the fix and I may have even spelled it back to them. We were now direct to RADDS. Later into the flight another controller asked us where we were going. I replied we had last been cleared direct to 'RADDS.' They said that had not been correct and that we should be going to what sounded like 'rats' and then cleared us to CUDLE Q117 SAWED Q97 ZJAAY JIMMS4. Out of curiosity I asked to clarify which fix was 'rats.' The fix they were referring to was RAPZZ. Both the pilot flying and myself were very sure we had heard RADDS spelled out and/or spelled back RADDS. Such similar sounding fixes on the same route contributed to this mix up. I had made an extra effort to spell out the fix when we finally found it just to alleviate any such confusion.