CAPT OF AN LTT FAILED TO HOLD SHORT OF AN ACTIVE RWY DURING TAXI CAUSING AN ACR B737 TO GAR.

Narrative

AFTER FLYING FLT FROM GRR TO MDW; WE WERE INSTRUCTED TO TAXI OUR ACFT X FROM OUR GATE TO FBO (AN FBO ON THE OTHER SIDE OF THE FIELD) AND SWAP INTO ACFT Y FOR OUR OUTBOUND FLT. AFTER COMPLETING INTERIOR AND EXTERIOR PREFLTS; THE #2 ENG WAS STARTED AND I CALLED FOR TAXI 'ACR X NEED TO REPOS FROM FBO TO OUR GATE.' GND REPLIED; 'ACR X TAXI VIA TXWY Y AND HOLD SHORT OF RWY 31C.' I READ THE INSTRUCTIONS BACK TO GND AND THEN REPEATED THEM TO THE CAPT AND HE REPLIED 'ROGER.' DURING THE TAXI; THE CAPT ASKED FOR ME TO START THE #1 ENG. I RAN THE APPROPRIATE CHKLISTS AND WAS GUARDING THE FEATHER LEVER WHILE MONITORING THE ENG INSTS WHEN THE CAPT SAID 'OH NO; I SCREWED UP.' ONCE HE REALIZED WE WERE ON AN ACTIVE RWY HE HURRIED ACROSS TO THE OTHER SIDE. AN ACR ON FINAL WENT AROUND WITHOUT INCIDENT. GND SAID; 'ACR X YOU WERE INSTRUCTED TO HOLD SHORT OF RWY 31C.' I REPLIED; 'ROGER.' GND SAID TO 'CONTINUE VIA TXWY Y TO YOUR GATE.' WE REPLIED; 'TO THE GATE VIA TXWY Y.' AFTER TAXIING TO OUR GATE WE CALLED OUR DIRECTOR OF OPS AND THE TWR. WHAT CAUSED THE PROB: 1) ACFT SWAP WITHOUT MUCH TIME TO NEXT FLT. 2) ENG START DURING TAXI. 3) DISCONTINUE USE OF CONTINUING FLT NUMBERS; CAPT HEARD SECOND OUTBOUND FLT INSTRUCTIONS AND CONFUSED THEM WITH OUR NEW INSTRUCTIONS.