ZFW Controller described a confusing flight plan routing event that highlighted the differing operational procedures and route clearance interpretations between ZFW; ZKC and TUL TRACON; noting the processing issue must be fixed.

Narrative

[I was] working MLC-L alone [with] moderate traffic. Aircraft X's flight plan (in NAS) showed TUL.TUL157.LOSZY.XXX.J25.SAT.SKF. LOSZY intersection is not on J25; hence the XXX's. I queried TUL Approach what route they are showing on Aircraft X. They showed the same as us. I then ask TUL Approach what Aircraft X filed [and there was a] big pause. So then a discussion ensues in which the finer points of our verbal agreement; 'direct and descending inbound; direct the first fix departures;' are delineated. It seems TUL Approach may be under the presumption that 'direct the first fix' means whatever fix their computer spits out; as opposed to the first fix the pilot filed. Because our (ZFW's) computer only gets what Tulsa Approach's (ZKC's) computer tells it; and ZKC's computer overwrote whatever Aircraft X filed; we have no way to know what the first fix was. Based on the whims of the Controller at TUL; the pilot may or may not be proceeding direct to that fix. Compounding all these pre-existing ambiguities was the fact that ZKC's computer spit out; and our computer accepted; an incomplete route. So; time was spent engaging [the] pilot of [a] single-pilot military [aircraft]; increasing his workload. Time was spent heads-down trying to amend flight plan; time was spent with next Controller coordinating flight plan because this Controller eventually ran out of time; and of course time had been spent with previous Controller trying to determine where Aircraft X was really going. All this time could have been saved if this computer issue; which is known and has been known for years; was fixed.