Isn't that a difference between domestication and farming?

If you've domesticated certain animals for meat production, it means you've bred traits that make them efficient producers of meat. You can produce a lot more meat per unit resource input with chicken than with other birds, with pigs rather than deer, or with cows rather than moose.

A hundred and fifty years ago, wild game was much more a feature of our diets. People lived closer to the wilderness and supplemented their diets with animals they killed themselves, including squirrels or other small mammals, birds, the occasional deer or wild hog. And the markets sold a variety of wild game. The carnivorous diet used to cover a much wider range than it does today.

Over time, meat production techniques evolved and become more efficient, with a greater focus on those animals which can be most efficiently raised for meat. We pick animals that have the highest feed conversion ratios, that can most efficiently convert animal feed into weight gained. Besides, our own population has increased over 5 fold since then, and we simply don't have enough land to feed everyone on wild game.

Meanwhile, our seafood production still largely relies on wild catches. We don't breed them to produce more meat per cubic foot of seawater. The limit is set by how much we can harvest in a sustainable manner without making the species extinct in short order. This requires that we diversify our catches if we want more seafood.

This is changing as aquaculture becomes a bigger source of fish. And the same trend will appear in seafood as well, with the range narrowing to fewer species. Already, the fish market is very heavy in farmed species like certain carp, tilapia, salmon, trout, catfish. As wild catches continue to fall and farmed fish production continues to rise, you'll increasingly find only the farmed species at your local fishmonger, and fewer of the wild caught species.