SF340 Captain reports communications breakdown with ATC during approach causing altitude deviations both leaving assigned altitude and attempting to return to it.

Narrative

The aircraft was established in a descent to 5;000 FT; our clearance was 'Pilot's Discretion to 5;000 FT.' As the aircraft descended; the Controller asked what approach we would like. The weather (330 degrees at 5 KTS; 9 SM visibility; broken 7000 FT) suggested that a visual approach was possible. We were still in IMC at about 5;800 FT so the First Officer and I reasoned that the visual was not such a good idea because the weather was not as the ASOS described. We decided that the ILS 35 was in order. I asked for the ILS approach and the Controller told us to expect vectors. After a brief pause; the Controller said 'radar contact lost.' There was not an audible call sign given and I assumed that he was still talking to us. He followed with 'you can fly the ILS on your own at 5;000 FT or climb to 6;000 FT for vectors;' we asked for the vectors/climb. The Controller said 'climb/maintain 6;000 FT vectors for the approach.' The altitude alerter was set to 6;000 FT and a climb was initiated. The Controller then gave a heading. The Controller then said 'aircraft X climb to 6;000 FT for vectors.' At that time we realized that the Controller was talking to someone else. We corrected the altitude alerter and initiated a descent to 5;000 FT. At 4;800 FT the First Officer and I noticed the altitude deviation and shortly thereafter the Controller questioned our altitude; due to the fact that the ALTS didn't capture. A correction was initiated but not fast enough; the aircraft continued in a descent. The autopilot was deactivated and a manual recovery was started. The aircraft captured 5;000 FT and the flight to ZZZ and the subsequent flight ZZZ1 continued unimpeded. This event happened because of changing weather conditions; both pilots selecting approach plates at the same time and the omission of inaudible call sign leading to conflict of instructions. Incidentally; the actual weather was broken 4;300 FT and 6 miles visibility.