When using depth of field and hyperfocal calculators, I get very different result versus the in-camera DoF preview of my Fujifilm X-M1.
For example:
With DOFMaster (or any other online calculator), for a Fujifilm X-M1, with a focal length of 16mm and f-stop = 8, I am supposed to get hyperfocal distance at 1.62 meters with DoF from 0.81 meters to infinity.
If I use those settings on the camera, in-camera DoF preview shows that DoF is about from 1.2 to 2.5 meters.
What am I missing?
First, a word about what depth-of-field is and is not:
In a way, depth-of-field is an illusion. There is only one plane of focus. Everything in front of or behind the point of focus is out of focus to one degree or another. What we call DoF is the area where things look, to our eyes, like they are in focus. This is based on the ability of the human eye to resolve certain minute differences at a particular distance. If the slightly out-of-focus blur is smaller than our eye's capability to resolve the detail then it appears to be in focus. When you magnify a portion of an image by making it larger or moving closer to it you allow your eye to see details that before were too close together to be seen by your eyes as separate pieces of the image.
Since things are gradually blurrier the further they are from the point of focus, as you gradually magnify the image the perceived depth of field gets narrower as the near and far points where your eyes can resolve fine details moves closer to the focus plane.
Since depth-of-field is dependent upon viewing size and distance as well as the visual acuity of the viewer it is hard for a camera to indicate depth-of-field if it doesn't know what the display size of the photo will be. Any in-camera DoF measurement is going to be based upon an assumption regarding the eventual viewing conditions of the photograph.
Assuming the standard 8x10 viewed at 10 inches by a person with 20/20 vision is probably a little too broad in the current digital environment. But most of the online calculators still assume this standard viewing size and distance. If you expect to view images at a 1:1 pixel size on a computer monitor, the DoF for the same exact image will be much narrower. After all, viewing a 22MP or so image on a monitor with 96ppi pitch is like viewing a part of a 60x40 inch print!
What am I missing?
You're missing that Depth of Field is subjective. In actuality, there's only one plane that's in focus — everything else can't be. Then, there's an area around that plane that is indistinguishable from out of focus because it's beyond the technical limitations of your camera to distinguish from perfectly in-focus. But, that's often quite small, too. Outside of that, it's a matter of how much blur you're willing to consider in-focus.
Sounds like your camera is simply more strict than the numbers used by the online calculators. I'm not seeing the X-M1 in DOFMaster as a pre-selected camera option, but I note that when choosing the X-Pro1 or X100, which use the same sensor, the calculator chooses a circle of confusion of 0.02 mm. That's giving me slightly different numbers than the near limit of 0.81 m which you say you get, but turns out I see that with a CoC of 0.019 mm, so I bet your other calculator is using that value for Fujifilm. (Or, it might just be rounding errors — with TawbaWare's calculator I get your values with CoC of 0.02 mm.)
On the other hand, if you chose a circle of confusion of around 0.007 mm, then you'll see values like Fujifilm is giving you in-camera. So, there's your answer in technical terms — Fujifilm has chosen a much more discerning value for CoC than the online calculators assume. (This value gives a hyperfocal distance of about 4.6 meters at 16mm and f/8, by the way.)
Film Format Basis vs. Pixel Basis
The depth of field (DoF) is the region in which, due to optical physics, a point has, on the film or the sensor, an image smaller than the size of the circle of confusion (CoC).
The CoC is "classically" determined from the accuracy of the human eye and the distance at which a given size image will be looked at, a common assumption is that the viewer will be at a distance equal to the diagonal of the image. This is the approach of the film format based DoF, taken by lens manufacturers even Fujifilm takes this path for Fujifilm X lens and DoF calculators. The CoC standard value for a full frame 24/36mm film is set to 0.03mm, and the equivalent CoC for a Fujifilm APS-C size is 0.02mm.
But, in a digital camera, you can also have the other approach, you could set the CoC to get the maximum use of your sensor taking in account its pixel size. This is the path Fujifilm takes when it calibrates the CoC for the viewers DoF indicator at 0.007mm
On its latest camera X-Pro2 and X-T2, Fujifilm gives you the option to choose one or the other value : "Film Format Basis" / "Pixel Basis"
