RPTR INVOLVED IN A RWY INCURSION CLAIMS TXWYS AT JFK ARE CONFUSING BECAUSE OF SIMILAR DESIGNATORS.

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WHILE HOLDING SHORT ON TXWY A OF THE ECHO INTXN; WE WERE GIVEN INSTRUCTIONS TO TURN L ON ECHO FROM THE TXWY A AND THE HOLD SHORT OF ZA. I READ BACK THE INSTRUCTIONS. BEING THAT ECHO WAS ON FIRST L AND ZA WAS VISIBLE TO THE L WE PROCEEDED ACROSS AN ACTIVE RWY ON TXWY E. I HAD MY HEAD DOWN IN THE COCKPIT TO COPY THE INSTRUCTIONS AND I WAS PREPARING THE GPS/RNAV FOR DEP. WHEN MY CAPT CALLED FOR 'CLR R' WE WERE ROLLING ONTO THE RWY AND WE SAW TFC INBOUND FOR LNDG APPROX 3/4 MI OUT. THE CTLR THEN TRIED TO CALL US FOR HOLD SHORT; BUT IT WAS TOO LATE AND THE ACFT ON FINAL EXECUTED A GAR. THE CONFUSION OF TAXI INSTRUCTIONS STEMS FROM SIMILAR CALLS AND TXWY DESIGNATORS. FOR INSTANCE THERE ARE TXWYS K AND A; AND KA. OFTEN INSTRUCTIONS ARE READ SO RAPIDLY THAT CONFUSION BTWN TAXIING TXWYS K; A; OR KA CAN OCCUR AND IN OUR CASE WE SHOULD HAVE VERIFIED THE INSTRUCTIONS. MY CAPT ASSUMED THE INSTRUCTIONS WE RECEIVED WERE CORRECT AND BELIEVED THE CTLR WANTED US TO CROSS THE RWY BEFORE TFC WAS A FACTOR. CALLBACK CONVERSATION WITH RPTR REVEALED THE FOLLOWING INFO: RPTR STATED THE ARPT WAS CONGESTED WITH TFC ON THE DAY OF THE INCIDENT AND THE CTLR WAS SPEAKING VERY FAST. DOES NOT GO TO JFK VERY OFTEN; ABOUT 5 TIMES THIS YR. WAS SURE SHE RECEIVED AND READ BACK TAXI INSTRUCTIONS CORRECTLY.