AAFCO statement

The two wordings

"Formulated to meet the nutritional levels established by the AAFCO Dog (or Cat) Food Nutrient Profiles" means the recipe was calculated against a table. No animal necessarily ate it before it shipped.

"Animal feeding tests using AAFCO procedures substantiate that this food provides complete and balanced nutrition" means a group of animals was fed the food for a defined period under a protocol, with bloodwork and body-condition checks. It is more expensive and slower, which is why it is rarer.

Both are legal and both mean "complete and balanced". They are not equally strong evidence, and the bag gives you no help telling them apart beyond the wording itself.

What the trial does and does not prove

A feeding trial demonstrates that animals stayed healthy on the food over the trial period — it catches formulation and digestibility problems a spreadsheet cannot. It is a minimum-duration protocol on a modest number of animals, not a long-term outcome study, and it says nothing about whether the food suits your particular pet.

It also does not follow that a formulated food is deficient. Most food sold is formulated, including plenty from companies with serious nutrition teams. The trial statement is the stronger evidence where you can get it, not a pass/fail line.

Life stage is part of the statement

The same sentence names the life stage the claim covers: growth, maintenance, all life stages, or growth including large-size dogs. A food substantiated for maintenance is not substantiated for a puppy, and the large-breed-growth qualifier is a separate clause that matters specifically because of calcium.