Air carrier pilot reported that while enroute from SJU to MEM the flight crew was navigating to fix VANZE but their clearance was direct VENDS. The confusion was due to the similar sounding fix names.

Narrative

We were climbing out of SJU and talking to San Juan Center. First Officer (FO) was Pilot Flying (PF). Captain was Pilot Monitoring (PM). The controller cleared us to what we thought was VANZE intersection on the VANZE 3 arrival into MEM. Captain read back the clearance and then spelled out the intersection in the read back to ATC. We inputted direct to VANZE with abeam points in the FMC. We were eventually passed off to Miami Center. We had just checked in with our third Miami Center sector when the controller stated we were off course and asked us to verify were direct VANZE. We replied affirmative and spelled out VANZE again. The controller came back and told us our clearance was to VENDS; not VANZE and spelled it out. We suddenly realized we were about 21 miles north of the airway. The controller then issued us a full route clearance direct to VENDS and then mostly as filed in our original clearance.This was caused by two similar sounding intersections; a slight language barrier and missed read backs. The SJU controller did have a Spanish accent. That combined with our familiarity with the VANZE Arrival into MEM and unfamiliarity with the VENDS intersection enroute lead us to input that into the FMC. The controller missed our incorrect read back. Also we did not have any queries from the first 2 Miami Center sectors we talked to despite the fact we were obviously off course. It wasn't until over an hour had passed since we received the direct to VANZE clearance and we were 21 miles right of course that the 3rd Miami Center controller queried us and re-cleared us back to VENDS and our original routing. Double checking of clearances and read backs by both pilots and controllers especially if a flight plan route has similar sounding waypoints.