Tony, I think the pond is exactly like an aquarium, just a few more variables in play, and on a much larger scale!! Same with backyard koi ponds.
Your aeration system and any plants/algae in the pond act as the filter. Fish in/fish out. Food in - waste has to be filtered out. Too many fish per gallon of water = dead fish.
Too much algae growing on things = reduce the amount of sunlight or the amount of nutrients in the "tank".
Yes, that's simplified, but the principle is the same.