Ok the thing to look for in these products is the word Derivitives.
Basically yes it comes from the product, however it's not the best part, usually the husks (in the case of rice n cereals)
or meat products usually the bits of the animal that couldn't be used for anything else.
Compare the Beta to the Barking Heads that we give ours.
BARKING HEADS BAD HAIR DAY LAMB & RICE DOG FOOD 2KG
Lamb & Rice hypo-allergenic, limited ingredient, fixed formula. Carefully formulated for all dogs, and especially those that have a sensitive skin & coat.
Ingredients:
Fresh Lamb (min 26%), White Rice (min 26%), Dried Lamb (min 26%), Ground Oats, Lamb fat, Salmon Oil, Whole Linseed, Minerals, Dried Tomato, Natural Seaweed, Glucosamine, Chondroitin, MSM, Vitamins.
Typical Analysis:
Protein 22%, Fat 16%, Fibre 3%, Ash 9%, Moisture 8%,
Vit A 13,500 iu/kg, Vit D3 1,200 iu/kg, Vit E (tocopherols) 400 iu/kg,
Copper (copper sulphate)12mg/kg,
Omega 6 (Linoleic acid) 3.1%,
Omega 3 (Linolenic acid) 1.0%
so you can see the difference
Animal derivitives (min 4%)
or 26% fresh lamb
The same goes for the rest of the ingredients.
However.
The better types are more expensive.
If your puppy has a sensitive stomach then you may have to have the expensive food.
If you are lucky and your pup has an iron constitution then the cheaper varieties may do them ok.