Q: Sentence (1) The object of my affection.
Sentence (2) Objects of thought.. Word: object.
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A: the same meaning

Q: Sentence (1) They saw the light of the beacon.
Sentence (2) He stopped the car and turned off the lights.. Word: light.
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A: different meanings

Q: Sentence (1) Run a new program on the Mac.
Sentence (2) They ran twenty blood tests on me and they still don't know what's wrong.. Word: run.
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A:
the same meaning