This is a good topic, many get it confused. Just because something is canned, does not mean it is “processed”. I have several examples here to describe these terms.
Processed. Think processed cheese slices, they are so processed, they cannot even be called cheese! Cheese Slices, Processed Cheese Food, things like that, it is closer to plastic than it is cheese. If the ingredients are more than 3 items (milk, rennet, salt) then you are talking about processed cheese.
Processed. Think canned condensed soups (I have another post on this site about that), The main ingredient in condensed soups is water, the label states less than 2% milk, the shortcuts I have for condensed soups, the main ingredient is evaporated milk, world of change there.
Prepared. Think canned beans. Nearly every time, this is beans, water, and salt. Think about it this way, if you take dry beans (like canneries do), and cook them in water (like canneries do), and add a pinch of salt (like you and I would do), that is a prepared beans, not processed. If you cook beans, you do the same exact thing minus the can. There is basically no differences in nutrition between canned and dry beans. Prepared would be also be canned vegetables or even frozen vegetables. You may pay a higher price due to the cutting of the vegetables and canning. I keep canned vegetables on hand for emergencies.
Prepared. Think canned tuna. I like tuna but I do buy them whole and cook myself, cheaper than canned, but it is the same, it is just cooked fish. You can make more cans of tuna from a 16-18 inch tuna for half the price. I keep canned tuna on hand for emergencies.