SIMILAR SOUNDING NDB AND ARPT CAUSED CTLR CONFUSION AS TO WHAT PLT WAS DOING.

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MY STUDENT AND I WERE PRACTICING APCHS. OUR RTE WAS FROM RNT TO PWT TO TIW TO RNT. PRIOR TO OUR APCH AT PWT; SEA APCH ASKED US FOR OUR REQUEST AT PWT AND WHAT WOULD FOLLOW. I REPLIED THAT WE REQUESTED AN NDB HOLD AND NDB AT PWT; THEN AN ILS AND NDB AT TIW. FOLLOWED BY AN NDB AT RNT. PRIOR TO THE ILS AT TIW; APCH ASKED WHAT FOLLOWED THE ILS; AND I REQUESTED AN NDB AT TIW AND AT RNT. ON OUR ILS MISSED APCH; WE WERE ASKED WHAT WE WANTED NEXT; AND I ANSWERED THAT WE WANTED TO GO TO GRAYE FOR THE NDB; MEANING DIRECT TO THE GRAYE NDB FOR THE FULL NDB RWY 35 AT TIW. WE WERE CLRED DIRECT GRAYE; AND THEN CLRED TO CROSS THE BEACON OUTBOUND AND CLRED FOR THE APCH. MY STUDENT READ BACK THE CLRNC. AS WE TURNED INBOUND FROM THE PROC TURN; I CALLED APCH TO GET A MISSED APCH INSTRUCTION AND FREQ CHANGE. THE CTLR RESPONDED THAT IT LOOKED LIKE WE WERE FLYING THE NDB AT TIW; NOT GRAY (ARMY AIR FIELD)! I TOLD HIM THAT WAS RIGHT; THAT WAS WHAT WE WANTED. HE SAID -- NO PROB AND CLRED US FOR THE NDB RWY 35 AT TIW. I CAN UNDERSTAND WHAT HAPPENED. MY REQUEST 'DIRECT GRAYE FOR THE NDB' WAS EASY TO MISUNDERSTAND (THE CTLR WAS WORKING 2 FREQS; 1 WITH MIL TFC AT TCM ON UHF). GRAYE AND GRAY SOUND THE SAME. ALSO; WE READ BACK THE 'CLRED FOR THE APCH;' WHICH WAS AN UNLIKELY CLRNC AT TIW WITH ITS OPERATING TWR; BUT LIKELY AT GRAY WITH THE TWR CLOSED. CALLBACK CONVERSATION WITH RPTR REVEALED THE FOLLOWING INFO: PPS AT SEA STATED THEY DO HAVE AN OCCASIONAL MISUNDERSTANDING ABOUT THE NDB AND THE ARPT BUT THIS IS GA PLTS UNFAMILIAR WITH THE AREA.