Wild salmon migrates between the the sea and the rivers. It is caught in these natural environments. Wild salmon is mainly consistent of muscles and less of fat, has the best taste, is leaner, but it is less heavy, less fatty and a bit less rich in flavour, but is is more nuanced and more refined. The best wild salmon I had in the 1980s living in Edinburgh where it was staple in these days; other fabulous wild salmon I ate in the 1980s was in Toronto and in Punta Arenas.
The worldwide stocks of wild salmon about halved in the past four decades. (1)
References: (1) https://www.sciencedirect.com/science/article/pii/S0308597X10002125 / https://doi.org/10.1016/j.marpol.2010.11.007,
see also https://www.healthline.com/nutrition/wild-vs-farmed-salmon#their-environments accessed 20/12/2019.
The annual production of farmed salmon has increased from 27,000 to more than 1 million metric tons worldwide in the last two decades (1). Farmed salmon has more fat, has more contaminants (2), and is often laced with antibiotics. Still, some farmed salmon is very good.
(2) Global assessment of polybrominated diphenyl ethers in farmed and wild salmon.
Environ Sci Technol. 2004 Oct 1;38(19):4945-9. or https://www.ncbi.nlm.nih.gov/pubmed/15506184 [Chilean salmon have the least, and European farms the most contamination, America is in the middle]; Risk-based consumption advice for farmed Atlantic and wild Pacific salmon contaminated with dioxins and dioxin-
like compounds. Environ Health Perspect. 2005 May;113(5):552-6.
Global assessment of organic contaminants in farmed salmon.Science. 2004 Jan 9;303(5655):226-9.
Contaminant levels in Norwegian farmed Atlantic salmon (Salmo salar) in the 13-year period from 1999 to 2011.Environ Int. 2015 Jan;74:274-80. doi: 10.1016/j.envint.2014.10.008. Epub 2014 Nov 9. [Good news: the levels decreased.]
See also https://www.healthline.com/nutrition/wild-vs-farmed-salmon#contaminants