In my opinion, you often don't make a difference and you can use what you want especially in the collocial language.
Though, if you want to be correct, here is an example which I consider as very memorable:
Lebensmittel: Apfel (apple -> food in his natural, untreated form)
Nahrungsmittel: Apfelmus (apple sauce -> treated food)
For more informations, just have a look: