Widebody Transport
Flight Crew Air Transport Pilot (ATP)
Communication Breakdown
ATC Issue All Types; Deviation - Track / Heading All Types; Deviation / Discrepancy - Procedural Clearance; Deviation / Discrepancy - Procedural Published Material / Policy; Inflight Event / Encounter Weather / Turbulence
Air Traffic Control Issued Advisory / Alert; Air Traffic Control Provided Assistance; Flight Crew Became Reoriented; Flight Crew Requested ATC Assistance / Clarification
Airspace Structure; Human Factors
Filed route of flight: ZZZ [...] DRK GABBL HLYWD1 KLAX. ATC had previously cleared Aircraft X to DRK flight plan route. There was a strong line of thunderstorms extending from Kansas down to Texas; so we asked for weather deviation south of course.  We were assigned 'direct to San Angelo; SJT; then Newman flight plan route'. The FO (First Officer) read back 'cleared direct SJT; Newman; flight plan route. Approaching SJT we required additional airspace south of course for weather deviation. We confirmed heading with ATC and were cleared direct Newman when able. The waypoint NWMAN is a point on the HLYWD1 Arrival on our filed flight plan release. I think the FO read back the phonetic NWMAN to the controller but there was no response. About 20 minutes after being cleared direct to point NWMAN; ATC assigned a 260 heading and queried what clearance we were provided.  The controller told us we were off course.  We responded with our clearance direct NWMAN flight plan route. As we looked at the enroute chart; we noticed there a was a VORTAC called Newman labeled EWM near ELP.  This point was not on our flight plan release; but this is when we realized the previous controller meant the VORTAC Newman not the point on our flight plan release labeled NWMAN.  We were then assigned direct DRK flight planned route. Both the Ft Worth and ABQ ATC controllers were understanding; professional and very cordial during the process. The FT Worth ATC radios were very busy with many aircraft asking for weather deviations. The radios were very busy and difficult to understand at times due to the weather.  There is a waypoint and a VORTAC named Newman.  They waypoint was on our route of flight. Use phonetic for VORTAC and names for the waypoint.  If using the name of a VORTAC then state the name and follow with the word VORTAC to differentiate between a VORTAC and a waypoint.
Air carrier Captain reported a navigation deviation due to a waypoint and VORTAC homonym.