B737-800
Flight Crew Air Transport Pilot (ATP)
Communication Breakdown
ATC Issue All Types; Deviation - Track / Heading All Types; Deviation / Discrepancy - Procedural Clearance
Air Traffic Control Issued New Clearance; Flight Crew Became Reoriented; Flight Crew Returned To Clearance
Human Factors
We were flying the CONLE1 departure (to the south); and taken off of that departure via 260 heading. There was traffic in the vicinity and weather further south. After the vector we were cleared direct what we thought to be DIW (Dixon) which joined AR22 and the remainder of our filed route. It was early in the morning and this would be logical to keep us away from the weather.We were then issued a frequency change. After checking in with the new Controller; he asked where we were cleared to. We stated DIW (Dixon). He then checked with our previous Controller and to us we were cleared by the previous controller to the fix DIXXE which was the next to the last point on the CONLE1 departure.  There were no traffic conflicts we were aware of. Both the Captain and myself understood DIW (Dixon) to be the cleared point; as it made sense with the vector off course and the weather needing to be avoided.The fix DIXXE is easily confused with the name of the older dual NAVAID VOR/ADF named DIXON (DIW). Two similar sounding names which are on the same flight plan and common flight path could easily be mistaken over the radio. Phonetics might be helpful; but a name change for the fix in this case might be more appropriate.
B737-800 First Officer reports being vectored off the CONLE1 Departure for traffic then cleared direct Dixon (DIW). The next Controller questions the heading and discovers the crew was actually cleared direct DIXXE on the CONLE SID.