A DH8B CREW DEPARTED EUG WITH THE WRONG ACFT.

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OUR CREW ARRIVED AT EUG ARPT AT XA45. WE WERE TO CREW THE XB50 DEP TO PDX. I USUALLY LOOK AT THE RELEASE AS SOON AS I AM HANDED IT. HOWEVER; UPON ENTERING THE OPS ROOM; OUR FLT ATTENDANT ASKED THE OPS AGENT WHICH ACFT WE HAD. THE AGENT RESPONDED BY SAYING WE HAD ACFT X AND THAT THE MINIMUM TOTAL FUEL TO PDX WAS 2400 LBS. SHE THEN HANDED ME THE RELEASE. SHE WAS NOT SURE HOW MUCH FUEL WAS ON ACFT X AND ASKED ME TO CALL HER ON THE RADIO IF WE NEEDED ANY. SHE LET US OUT TO THE RAMP AREA. WE BEGAN DOING OUR NORMAL PREFLT DUTIES. ACFT XPH WAS PARKED IN THE NORMAL PLACE FOR THE PDX DEP FOR THAT TIME OF DAY. FROM THE RELEASE; I CONFIRMED THE WX AT EUG AND PDX AND CONFIRMED THAT OUR ACFT HAD THE MINIMUM TOTAL FUEL OF 2400 LBS FOR OUR FLT TO PDX. MINIMUM TOTAL FUEL AND OPTIMUM FUEL WAS 2400 LBS PER THE RELEASE. FUEL WAS NOT NEEDED. THE OPS AGENT ASKED IF WE WERE READY TO BOARD. THE FLT ATTENDANT SAID SHE WAS; SO I GAVE THE GO AHEAD TO DO SO. ALL BOARDING WAS ACCOMPLISHED NORMALLY. I COMPLETED THE LOAD MANIFEST AND BEGAN THE BEFORE START CHKLIST. ENG START FOLLOWED. DURING ENG START; THE OUTBOUND CREW FOR SEATTLE WALKED BY OUR ACFT AND WAVED. WE RETURNED THE FRIENDLY 'GOOD MORNING;' THEN WALKED TO ACFT YPH AND BEGAN THEIR PREFLT AS WE TAXIED OUT. AFTER DEP; I CALLED EUG OPS TO GIVE MY OUT AND OFF TIMES. THE OTHER CREW IN EUG WAS ON THE RADIO AND WAS TELLING THE OPS AGENT THAT 'YOU DON'T UNDERSTAND; ACFT X IS ALREADY GONE -- THEY'RE AIRBORNE.' I THEN BEGAN TO WONDER WHAT WAS GOING ON. IT THEN DAWNED ON ME THAT I MAY HAVE TAKEN THE WRONG ACFT. ONLY THEN DID I LOOK AT THE ASSIGNED ACFT ON THE RELEASE. IT CONFIRMED MY SINKING FEELING IN MY STOMACH. INDEED; I HAD DEPARTED WITH THE WRONG ACFT. I IMMEDIATELY CALLED DISPATCH IN PDX AND INFORMED THE DISPATCHER WHAT I HAD JUST DONE. WE AMENDED THE RELEASE TO REFLECT ACFT XPH. THE ACFT CONFIGNS WERE ADJUSTED AND I AMENDED THE LOAD MANIFEST TO REFLECT THE SMALL REDUCTION IN ACTUAL TKOF WT. THE FLT CONTINUED TO PDX. LATER THAT MORNING; I WENT TO THE DISPATCH CENTER TO APOLOGIZE. THEY WERE SYMPATHETIC TO MY SIT. THEY TOLD ME THAT INDEED; A PLANE SWAP HAD OCCURRED IN EUG; AND THAT THE OPS AGENT AND GND PERSONNEL MUST NOT HAVE BEEN ADVISED OF IT. ACFT X SHOULD HAVE GONE TO SEA AND ACFT Y SHOULD HAVE GONE TO PDX. THE RELEASE SHOWED THE PROPER ACFT; BUT I DID NOT CONFIRM THE TAIL NUMBER UNTIL IT WAS TOO LATE. SEVERAL EXTENUATING CIRCUMSTANCES SEEMED TO PLAY A PART IN THIS SIT. FIRST; I DID NOT CONFIRM THE TAIL NUMBER ON THE RELEASE BECAUSE OF WHAT THE OPS AGENT HAD TOLD US. SECOND; NONE OF THE GND PERSONNEL CAUGHT THE CHANGE IN ACFT ASSIGNMENT. ALL THE PDX BAGS WERE BOARDED ON MY ACFT. ALL THE PDX PAX WERE BOARDED ON MY ACFT. THIRD; THE ACFT WAS PARKED IN THE SAME NORMAL SPOT THAT IT ALWAYS IS FOR THIS FLT TO PDX. FOURTH; MY FO DID NOT CATCH THIS ERROR ON HIS RELEASE COPY EITHER. HE ASSUMED THAT ACFT X WAS TO GO TO PDX JUST AS WE WERE ADVISED. FIFTH; THE OUTBOUND CREW TO SEA JUST WALKED BY AND WAIVED AT US. THEY WERE NOT AWARE OF THE SIT UNTIL AFTER WE DEPARTED. I UNDERSTAND THAT I AM ULTIMATELY RESPONSIBLE FOR ALL THE PREFLT ACTIONS FOR A FLT; AND THAT I LACKED IN PROPER ACFT ASSIGNMENT. I FEEL THAT ONE WAY TO STOP THIS FROM HAPPENING AGAIN (IT HAS HAPPENED BEFORE) IS FOR THE OPS AGENTS TO REFER CREW MEMBER QUESTIONS ABOUT ACFT ASSIGNMENTS BACK TO THE PIC. THIS WOULD FORCE THE PIC OR SIC TO LOOK AT THE LEGAL DOCUMENTS AND CORRECTLY IDENT THE ACFT ASSIGNED TO THEM.