Multi-class classification assigns a single object to one of several possible classes.
In your fridge example - if your classes are distinct categories, like 'apple', 'cheese', 'banana', etc., then you would be looking at a multi-class problem. An apple would be assigned a class 'apple' and salmon - 'salmon'
Multi-label classification assigns a single object to several possible classes.
In your fridge example - if your classes overlap, like 'vegetarian', 'safe for kids', 'meat', 'fruit', etc., then you would be looking at a multi-label problem. An apple might get assigned classes 'vegetarian', 'fruit', 'safe for kids', and salmon would get 'fish', 'safe-for-kids'.