John,
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Your radio was made in 1973. There were no FT-101 radios (with no suffix) made in 1983. The last 5 digits of the number on the back plate are the actual serial number, so 33037 in your case. It must have been a very late model, just before the FT-101B came out.
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To see the other serial number you would have to take the outer case off. It is on the side chassis adjacent to the crystal bank / driver area. This number may or may not match the number on the rear panel.
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73,
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Peter
G4DJB
