PLT IN SMA TYPE ACFT AFTER LNDG TAXIED ONTO RWY 24 AT PWK WHILE A PIPER NAVAJO WAS DEPARTING.

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NEW PLT TO ACFT IN L SEAT. PNF IN R SEAT. TWR GAVE CLRNC TO LAND WITH LAHSO. DUE TO PF LOW TIME IN TYPE; PNF REFUSED LAHSO. NEW CLRNC TO LAND GIVEN. ON LNDG ROLL; CLRNC GIVEN TO TAXI OFF ACTIVE; THEN TAXI ON RWY 12; HOLD SHORT OF RWY 24 FOR DEPARTING TFC. ACKNOWLEDGED CLRNC BUT WENT PAST RWY 12. SIGN WAS CONFUSING AND PF ASKED 'TURN HERE?' PNF SAID 'DO NOT TURN HERE;' INDICATING WHAT PNF THOUGHT WAS TXWY BUT WAS ACTUALLY RWY 24. CTLR HAD CLRED AN ACFT TO DEPART RWY 24 AFTER WE ACKNOWLEDGED OUR TAXI CLRNC. HE TOLD PNF THAT HE WAS LOOKING AT NEXT APCH WHEN WE TURNED ONTO ACTIVE RWY 24. ACFT ON RWY 24 (A NAVAJO) SAID THERE WAS NO PROB; HE WAS CLR OF US. TWR CTLR SAID HE WOULD NOT FILE RPT OF INCURSION. WE SHOULD HAVE STOPPED ON ACTIVE AND ASKED FOR CLARIFYING INFO BEFORE WE PROCEEDED; AS BOTH PF AND PNF DID NOT AGREE ON TAXI INSTRUCTIONS AND WHERE WE WERE LOCATED ON ARPT. CTLR GAVE GOOD CLRNC; BUT SHOULD NOT HAVE LOOKED AWAY FROM DEPARTING ACFT WHEN HE CLRED IT TO TAKE OFF UNTIL HE WAS SURE THERE WAS NO CONFLICT.