word choice - Difference between 区別 and 分別

Can anyone here help me understand the difference in nuance between 区別 and 分別 (in terms of the 'classification/distinction' meaning)? I have checked dictionaries but they seem pretty much the same in this case. I would have considered them interchangeable had I not just gotten a question about the difference wrong in a mock test.

Answer

Basically 分別 is used only in the following two types of situations:

• separating trash (flammable, recyclable, etc); read [ぶんべつ]{LHHH}
  

  
  

  
  
  • 燃えるゴミと燃えないゴミを分別する
  
  
  • ゴミの分別収集にご協力ください
  
  
  • 空き缶は分別してリサイクルしましょう
  
  

  
  

  
  


• distinguishing the right and the wrong as a sensible adult, discretion; read [ふんべつ]{HLLL}
  
  

  
  

  
  
  • 物事の分別が分かる年齢になった
  
  
  • 良いことと悪いことの分別をつける
  
  
  • 大人としての理性と分別を身につける
  
  

  
  

  
  

According to BCCWJ these two usages are almost equally common. There were a few other examples using 分別 (apparently about philosophy or psychology), but I think you can safely ignore them.

区別 is "distinction" in general.