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To the best of my knowledge I think work function and threshold energy are the same because they both represent the minimum energy needed to remove the electron form the metal surface.
I think for our purposes the two terms can be used interchangeably. However, I believe work function describes the minimum amount of energy needed to eject an electron, and threshold energy is used when talking about the frequency required to eject an electron.
When you see it on quizzes or tests, they basically mean the same thing. When light hit the surface, the photon energy (from the light source) has to be bigger or equal to work function/threshold energy in order to remove the electron.
Essentially they are the same thing. The work function describes the work being done to remove an electron. Since work requires energy, it can be said that the threshold energy is the energy required to do the work of removing an electron.
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