Circumstances VH-FRI was carrying out airwork at Wagga and was preparing for a practice VOR/DME approach to runway 05. Wagga air traffic control (ATC) were using runway 23 as the runway in use and this was also the runway to which most training aircraft were making their approaches. At 1235 hours the pilot of VH-FRI requested a runway 05 VOR/DME approach and ATC replied that he could expect a runway 23 VOR/DME approach and wrote this detail on the flight progress strip. The two crew members in VH-FRI did not realise that the controller had issued an expectancy for a different runway to that requested and continued to position their aircraft for an approach to runway 05. At 1244 hours ATC approved VH-FRI to make a sector entry for a runway 23 VOR/DME approach. Again the crew did not notice that the runway given was not the one requested. The controller passed overshoot instructions to VH-FRI that would keep that aircraft clear of VH-WGX which was approaching Wagga on a flight from Albury and had been instructed to track for a landing on runway 23. The cloud was five octas at 2,000ft and therefore a visual sighting by ATC was not guaranteed. However the controller had sighted VH-WGX at approximately 5 - 8 NM from the field and he continued to look for VH-FRI in the same direction but nearer to the runway as VH-FRI was sequenced to be first. At 1259 hours the controller had still not sighted VH-FRI and decided to look in the direction of the runway 05 final approach and saw VH-FRI commencing an overshoot on that runway. He immediately issued new instructions to both aircraft that maintained visual separation standards and a breakdown in separation was averted. Significant Factors 1.The crew of VH-FRI, having requested runway 05, continued to hear runway 05 even though the controller was saying runway 23. 2.The air traffic controller, having expected a request for runway 23, misheard the pilot request an approach for runway 05 and continued to issue instructions for a runway 23 approach procedure.