What does 'Naturally smoked' fish mean?

I visited the 'Burren Smokehouse' in Co CLare, Ireland last year. I watched them 'naturally smoke' the salmon. Here is link to their process. Hope this helps.
http://www.burrensmokehouse.ie/blog/about/life-cycle-of-the-wild-salmon/how-we-smoke-our-salmon

Thanks to all who answered. More and more imported goods, so sometimes its hard to know distinctions.

Many people see the term "liquid smoke" and assume it's artificial but it's simply natural wood smoke that has been processed for convenience, utility and economy. Used properly, you won't know the difference. And it's everywhere in the industry. You've probably been consuming it all your life without knowing it.

Artificial smoke is a different story. I'm not a food chemist and I don't know all of what's involved with the stuff but my opinion is it's best to stay away from it. Fortunately, at least in the U.S., it must be clearly labeled "artificial smoke flavor":

"No representation may be made, either directly or implied, that a food flavored with pyroligneous acid or other artificial smoke flavor has been smoked or has a true smoked flavor, or that a seasoning sauce or similar product containing pyroligneous acid or other artificial smoke flavor and used to season or flavor other foods will result in a smoked product or one having a true smoked flavor."

Now I'm really puzzled. I agree with la domestique that artificial smoke sounds yuck! But after reading ChefOno's answer, I don't know. And if liquid smoked product can carry the term 'Smoked' how do you tell the difference?

The line between natural and artificial is open to debate -- except not when it comes to food labeling requirements. The U.S. FDA very specifically regulates the terms (and other countries have similar requirements).

As for smoke flavorings, there are both natural (derived from real wood smoke) and artificial varieties.

The term "Naturally Smoked" indicates the product has been "exposed to smoke generated from burning hardwoods, hardwood sawdust, corn cobs, mesquite, etc.", i.e. the traditional smoking process as opposed to the use of liquid smoke (which can carry the term "Smoked").

However…

The argument could be made that foods smoked over wood are less healthful than foods flavored with liquid smoke products. Tars, ash and other undesirable byproducts are removed during production of liquid smoke but presumably remain when smoked over wood.

It means nothing . . . there is no regulated definition for the work natural in the food industry, so anyone can make up their definition. I would not trust the claim. Only Organic is regulated and defined.

I agree with jmburns- naturally smoked fish is actually smoked over wood chips or some other material (be it cold smoked or hot). Some smoked fish you will find at the store is injected with artificial smoke flavor- yuck.

I would assume it means that it was not flavor enhanced with chemicals or flavoring like Liquid Smoke.