You need to give the Heritage Center the TS number that is on the Commission Number plate. If you have the correct and original plate, it's possible that the number on yours may be correct. But many number plates were swopped by previous owners just to get a TR title that would be accepted. Mine reads TS 27489 LO and is the original plate that came with my 1958 TR3A when I bought it brand new in May, 1958. The "L" is for "Left hand drive" and the "O" indicates it left the factory with the overdrive option installed.
New blank Comm. No. (VIN) plates are available from the usual TR parts suppliers, but the printing fonts are different, so if the fonts on your plate look identical to mine it means that your plate came from the factory on a new TR. It might mean it came on your TR or on another TR.
The number on the engine should be about 300 to 400 numbers higher because Standard-Triumph sold some TR engines to Morgan. This the second clue.
My engine number is stamped into the side of the engine block on the flat milled spot just to the rear of the distributor. Mine reads reads TS 27789 E (The "E" is for Engine). If your numbers are this close, there is a strong probability that these would be considered "matching numbers" by the judges at a TRA concours event.
My EB number above the battery box reads EB 27710 which is another clue.
You don't need to concern yourself about the number on the frame (like Z 28) or the ones on the differential, the gearbox or the overdrive casing.