So when I go to the market and get "Wild Caught Salmon" it really could be farm raised salmon that escaped and were subsequently fished in the vicinity?
I would be highly suspicious of anything calling itself "wild" and "Atlantic" in the same breath. There is almost no wild Atlantic salmon fishery left in the United States and Canada. It's all farm raised. Occasionally you can find legitimately wild Atlantic catch in Scotland or Norway. But wild catch makes up less than 1% of all Atlantic salmon on the market.
So if you want wild salmon, start by looking for a Pacific label, a listed species, or a regional designation of some kind. That's still not a guarantee, but it narrows things down quite a bit.
For what it's worth, 90% of all salmon on the US market is farmed. So if you're at a restaurant or a BBQ and aren't sure what you're getting, you're probably getting farm-raised Atlantic salmon.
For me Atlantic vs Sockeye or Copper River Salmon. Atlantic is usually a faded pink orange color. It’s more like Arctic Char. Pacific Sockeye is extremely red.
Another fact, the only native Trout species in my state, Georgia, is Brook trout. They are actually closer to Arctic Char than trout or salmon.
Unless you caught it yourself, color is a particularly bad way to determine the kind of salmon you’re looking at; Fish farms feed their fish a steady diet of red dye to colorize their flesh: https://qz.com/358811/heres-why-your-farmed-salmon-has-color...
Kings, sockeyes and cohos. It's all caught in Prince William Sound near the mouth of the Copper River. I grew up fishing there. There is a lot of marketing, but I think it tastes way better than farmed or Atlantic salmon and just can't bring myself to eat that.
A caught fish could be wild, or from a hatchery. You can tell the difference since hatchery fish have a fin removed but I imagine it's easier to not differentiate when labelling.
I've always assumed that "Wild Caught" was used a purpose so the fish could be farmed, but then let loose and caught in the "wild". But maybe it's more difficult to do that.