What is "Food Grade" Stainless-Steel or Aluminum
Here's a description for Stainless Steel. It applies in Canada, but is likely similar elsewhere:

Grades of Stainless Steel that are Safe for Food
There are 150 grades of stainless steel, but your container, cup or plate should be made from one of these (check the label):
304
The most commonly used food-grade stainless steel; it is used in food, dairy, brewing, hospital and sanitation applications.
316
The second most commonly used food grade, it has the same uses as above, but has better corrosion resistance because it includes more nickel than 304.
430
Products made from this food grade generally have less nickel content and a lower resistance to corrosion and temperature. It’s best to dry these containers right after washing.
You may also notice that products will say 18/8, 18/10, 18/0 beside the grade. The first number is the percentage of chromium that is contained in the stainless steel. The second number is the amount of nickel. The higher the numbers, the more rust resistant the product will be. Nickel is safe in small quantities but can provoke a reaction in people with an allergy to it. The average adult consumes between 150 to 250 micrograms of nickel per day. Small doses of chromium, like iron, are good for your health, but can be harmful in higher amounts—50 to 200 micrograms per day is considered safe. One meal prepared with stainless steel equipment (such as stainless steel pots and pans) gives you about 45 micrograms of chromium, according to Health Canada.

And Aluminum is typically Alloy 1100:

Alloy 1100: This grade is commercially pure aluminum. It is soft and ductile and has excellent workability, making it ideal for applications with difficult forming. It can be welded using any method, but it is non heat-treatable. It has an excellent resistance to corrosion and is commonly used in the chemical and food processing industries.


Personal Opinion
It sounds like one of the biggest factors is corrosion resistance. My understanding of food grade materials is that they are mostly looking for material that is free of toxic materials (like lead, or nickel and chromium in higher quantities), and are resistant to harboring bacteria. By their nature, new aluminum and stainless steel meet these criteria, but the ones listed above provide more resistance over time.
I also couldn't find an official requirement, these seem more like guidelines that are followed by the food industry, possibly encouraged by a discerning public. Canadian Family, for example, recommends to check the label, suggesting some manufacturers don't follow these guidelines.