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I'm still looking for that swing that I can easily follow and pattern my swing...

I heard that Natural Golf and Swing Machine golf are both likened to the swing of the Iron Byron which was inspired by the swing of Byron Nelson...is this true?

If it is are they the same swing with different names?
Which one is better or easier to adapt or follow?

Swing Machine Golf is based on the way the Iron Byron swings a club, so that is correct. I've got the book and DVD's, and I'd say that it's a pretty good way to learn to play better golf. I haven't watched the DVD's yet, but the book is first rate in my opinion. I got to meet the author and he seemed to know what he was talking about. And it's not the same as Natural golf.

I am not familiar with Swing Machine Golf, but I do use the Natural Golf Swing. Here is what I do know. Moe Norman is credited with the term NATURAL GOLF, but he did not invent the method. Byron Nelson is the first to use the single plane swing method I know of, and it is exactly what is known as Natural Golf today. In addition Iron Byron is the machine all the club and ball manufactures use to test their equipment, and the machine is modeled after Byron Nelson’s swing. So IMO Byron Nelson, Natural Golf, and Iron Byron are directly related. My guess is Swing Machine Golf is just another marketing gimmick for Byron Nelson’s or Natural Golf Swing.

I'd recommend NG, it makes the swing much easier in my opinion and I've been playing increasingly better, I need to revisit the fundamentals but have found I can hit it pretty straight when everything is done properly. The thought process is so much easier than the traditional swing.

here's a great video on the differences between the two...

YouTube - The Real Single Plane Golf Swing - "Little Moe" explains

As Todd Graves explains in the video, the "single plane" (more properly called "single axis") concept in Natural Golf is not the same as "single plane" as understood in more traditional swing systems.

In NG not only the shaft is on the same plane during the whole swing but also the arms, which shape a "single axis" with the shaft.

That's why Moe Norman, compared to Byron Nelson, stood much farther from the ball. Other differences are: Moe was more tilted to the ball, he did a shorter backswing, he had much a wider stance, he gripped the club with the palms, not the fingers and he gripped it firmer.

I think Nelson and Norman's swings had very little in common, although both of them are "single plane" if you focus exclusively in the shaft trajectory.

Is Natural Golf an accepted method already by golfers or do "conventional" golfers still find it weird and not a legit golf swing? Any touring pros use Natural Golf?

Allen Doyle's swing resembles Moe Norman's. I don't know of any other tour pro who follows NG.

But there's no way to compare the effectiveness of NG against more traditional methods or styles, because the latter's followers outnumber the former's 100 to 1.