ACR FLC INCORRECTLY ASSUME TAXI INSTRUCTIONS AFTER LNDG SEA RWY 34L AND INCUR INTO RWY 34R CAUSING A TKOF ABORT.

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I HAD JUST COMPLETED A PRACTICE CAT III APCH IN VISUAL CONDITIONS. WE HAD BRIEFED AND WERE EXPECTING TO TAXI STRAIGHT OFF ON EITHER HIGH-SPEED TXWY K OR H. AS WE CLRED THE RWY ON TXWY H; SEATTLE TWR CLRED US TO: 'TURN R AND R AGAIN; HOLD SHORT OF 34R'. MY FO READ IT BACK AS: 'TWO RIGHT TURNS; HOLD SHORT OF 34R'. I DON'T BELIEVE THE CTLR USED TXWY NAMES IN HIS CLRNC; BUT I UNDERSTOOD THAT I WAS TO MAKE THE QUICK TURN ONTO THE INTERSECTING REVERSE HIGH-SPEED J; A GREATER THAN 90 DEG R TURN. AFTER COMPLETING THE TURN; I WAS SURPRISED TO SEE WHITE EDGE LIGHTS RAPIDLY APCHING. I LOOKED TO THE R; DOWN WHAT I NOW RECOGNIZED AS RWY 34R AND SAW THE HEADLIGHTS OF AN ACFT THAT HAD JUST BEEN CLRED FOR TKOF. I ASKED MY FO IF WE WERE CLRED TO CROSS; IMMEDIATELY REALIZED THAT WE WERE NOT AND APPLIED THE BRAKES TO STOP THE ACFT. OUR ACFT'S NOSE ENDED UP ABOUT 6 FT PAST THE RWY EDGE LIGHTS. I ASKED MY FO TO CALL THE TWR AND ADVISE THEM TO STOP THE TKOF OF THE OTHER ACFT; WHICH HE DID. THE OTHER ACFT ABORTED HIS TKOF AT WHAT APPEARED TO BE A RELATIVELY LOW SPEED AND TAXIED CLR; WELL S OF US ON EITHER TXWY N OR M. WE WERE THEN CLRED TO CROSS RWY 34R AND TAXIED TO PARKING WHERE I CALLED THE TWR AND GAVE THEM A BRIEF ACCOUNT OF THE INCIDENT. HUMAN FACTORS CONSIDERATIONS: 1. DISTRACTION: I FLEW A PRACTICE CAT III APCH FOR THE PURPOSE OF LOGGING IT FOR SELF-CERTIFICATION; CONCENTRATING ON FLYING A PRECISE APCH AND LNDG USING THE HUD. DURING THE FLARE; WE GOT AN 'APCH WARN'; WHICH WOULD HAVE REQUIRED A GAR HAD IT BEEN IMC. SINCE WE WERE IN VMC; I CONTINUED THE LNDG VISUALLY; ALTHOUGH THE HUD STILL APPEARED USABLE. I WAS STILL REVIEWING THE APCH AND LNDG IN MY MIND AS WE CLRED THE RWY. IN ADDITION; MY FO BECAME PREOCCUPIED WITH METHODICALLY COMPLETING THE AFTER LNDG CHKLIST AS SOON AS WE HAD CLRED THE LNDG RWY (34L). 2. FATIGUE: WE HAD BEEN FLYING IN THE EASTERN TIME ZONE FOR 3 DAYS AND HAD ARRIVED LATE THE NIGHT BEFORE. ALTHOUGH THIS WAS NOT AN EXTREMELY LONG DUTY PERIOD 9 HRS AND 35 MINS; THE INCIDENT OCCURRED AT THE END OF A LONG DAY. 3. EXPECTATION: I HAD BRIEFED AND WAS EXPECTING TO TAXI STRAIGHT OFF THE RWY AND HAD NOT ANTICIPATED A CLRNC FOR A HARD R TURN ONTO THE INTERSECTING REVERSE HIGH-SPEED TXWY. THUS THE CLRNC CAUGHT ME BY SURPRISE; AND AFTER THE TURN; THE ACTUAL VISUAL PICTURE WAS DIFFERENT FROM WHAT I HAD EXPECTED TO SEE. 4. COMMUNICATIONS: THE NON-STANDARD CLRNC WITHOUT SPECIFIC TXWY NAMES WAS A BIT CONFUSING; AND IT TOOK ME A MOMENT TO INTERPRET WHAT I WAS BEING TOLD TO DO. I BELIEVE I BECAME PREOCCUPIED WITH THE FIRST PART OF THE CLRNC (TURN R AND R AGAIN); WHILE THE SECOND PART (HOLD SHORT) DIDN'T COMPLETELY REGISTER IN MY MIND. IT'S NOW CLEAR TO ME THAT I BECAME MOMENTARILY OVERLOADED AND VULNERABLE TO MAKING AN ERROR. I NEED TO BETTER MANAGE MY WORKLOAD; ESPECIALLY WHEN I'M FATIGUED; AND WILL DO THE FOLLOWING: 1. I WILL NO LONGER PLAN PRACTICE APCHES AT THE END OF A DUTY DAY. 2. I WILL SPECIFICALLY INCLUDE IN MY APCH BRIEFING THE LOCATION AND PROXIMITY OF ANY ACTIVE RWYS TO BE CROSSED ENRTE TO PARKING. ADDITIONALLY; I WILL BRIEF MY CO-PLTS TO NOT RUN THE 'AFTER LNDG CHKLIST' UNTIL WE'RE CLR OF ALL ACTIVE RWYS AND IN CONTACT WITH GND CTL. 3. WHEN POSSIBLE; I WILL DECLINE SHORTCUT CLRNCS AND REQUEST TO STAY WITH THE SIMPLER ROUTING PREVIOUSLY BRIEFED.