word choice - which vs what usage

Which determiner, which or what, to use for some situations, like these:

• 
  

  What month is it? What school are you attending now?

  
  

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or

• Which month is it? Which school are you attending now?

I understand that which" expresses the idea that in the context of the sentence there is a list of possibilities to chose from.

"what" is more open-ended.

However, can there be a better distinction?

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