I once heard a comedian say he wondered why cat food doesn’t come in flavors like “mouse” or “sparrow”.
because pet food is really marketed towards people.
It depends on whether you mean corn is “a huge part of the diet” economically or nutritionally.
Saying that the corn a cow eats is part of my diet is just nonsense.
Both are really hard to raise for food (being so small). And, generally no one raises animals for cat food, they just use the meats us humans raise for ourselves.
Yes, the various brands packaging are simply changed on the fly without even stopping the machines. The same thing goes for almost everything from toilet paper to toothpaste. Some brands have proprietary formulas of their own that are used by the manufacturer but most of these brands do not produce their own food.
And really none of the dry dog and cat foods would even get eaten if it weren’t for the flavors that are sprayed on the kibble. These flavors are made out of a digest of usually chicken byproducts. Open a can of Campbell’s condensed chicken soup and you have an idea of what the typical pet food flavor looks like.
There is a lot of waste chicken viscera (guts) available in the major chicken processing areas like Missouri and Arkansas and pet food is where most of it goes.
For fish flavors the source is menhaden solubles from the gulf areas, Louisiana. Beef flavors are rendered from excess spleens and livers.
I cooked up many a tank car load of flavors back in the day.
We’ve had people here who worked at shelters state, in the past that they cremate the remains of animals put down, IIRC.
Well, note the part where I said “commedian”. 
But seriously, most pet food is made up of by products: lips, hooves, snouts, ears, etc. All the stuff we don’t want to eat.
I saw a segment on our local news about choosing pet food, and they talked to various vets, and they all said the two things you want to look for: make sure it says “Complete and balanced” and “approved by the Association of American Feed Control Officials” (I THINK that’s the name of it).
The AAFCO seal is important, although there are two ways of getting it, IIRC.
One is doing a complete food trial with the recipe and submitting the results and recipe to AAFCO. Usually done with higher-end brands and those that are for prescription only.
Other brands can get AAFCO if they provide a complete feed analysis of the end product and it meets the minimum nutritional requirements established for species and life stage.
I just feed my pets whatever whole, raw animal parts are on sale at the Asian market round the corner. Cheaper and easier than figuring out kibble.