Actually. You are wrong. The software is doing what you note in the 2nd picture. (You can check this in the layer view)
However, there are more factors from the material in play, which aren't compensated yet. Not sure how to call all effects. Shrinkage is a simple one. But there is also the tendency of hot material to "flow together" which causes inner circles to also be smaller then designed.
By the way, it's not just 3d printing that requires you to make the CAD model different from desired end result. This is true of injection molding where you even have to change angles, and cnc milling and so on. Other recommended alterations are in this amazing guide by IRobertI:
http://support.3dverkstan.se/article/38-designing-for-3d-printing
....The software is doing what you note in the 2nd picture. (You can check this in the layer view)
....
Would it be possible to add 3 variables, e.g. 1 for inner wall, 2 for outer wall and 3 for height, where a coefficient will be insert to compensate this. When printing technical parts that would be extremely helpful.
example: I print a square with a hole in it. So i could change the wrench width independently from the height and the hole diameter without the need for the original cad file. Like a normal cnc machine with tool-offset.
I am very glad to read that the "should be done" is ... already done.
But, as I said, I used to print on another 3D printer which is using proprietary software and I can insure you that the printing have "exactly" the same dimensions, inner or outer side (of course, in relation to the precision of the machine). This firm have been manufacturing cnc machine since a long time and they came to the 3D printing market.
When I look to my new printing using Cura comparing to the others, the internal dimensions of horizontal holes look like so "rought" that I cannot beleive that the inner side is calculated correctly.
That's why I really would like to understand why there are so much differences.
Is there any parameter I can change to have it better ?
Eric
Please tell us what printer you have, what firmware you are running and show us a picture of these rough surfaces, then we dont have to guess as much what to answer 
When I look to my new printing using Cura comparing to the others, the internal dimensions of horizontal holes look like so "rought" that I cannot beleive that the inner side is calculated correctly.
Well, I can tell you that it's calculated as you are suggesting. I made Cura, so I kinda know how it works.
There could be multiple reasons why the other software is producing correct results. (but it's only guess work from our side, due to the lack of information from you, like, which software, which printer, same printers?)
Could be just luck. Could be some heuristics (which I rather avoid due to the large range of material people are using)
Not sure what Cura does but outer dimensions are accurate while inner dimensions are completely off by 0.4mm (2x0.2mm) when using 0.2mm height with 0.4 nozzle. You can see by yourself already with a simple sketch in simulation mode. Make a square of 1.2mm perimeter. With 0.4 nozzle and 0.4 layer height you should have 3 lines side by side, but with with 0.2 layer height you should normally have only 2 (because material get squished on the side of the nozzle). Cura slicer is likely not accounting for that squish properly on the inside.
Using a 0.4 nozzle, we could probably attempt to solve it by using 0.6 line width.
REM: there is a hole expansion correction settings (expecting 0.2mm) but it is not working for inner part of an open shape.
ArunC posted a topic in UltiMaker 3D printers,
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ArunC posted a topic in UltiMaker Cura,
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gr5 2,192
What you describe "should be done" is "what is done". The thickness of the red stripe is typically your "nozzle width" but only if "shell width" is an integral multiple of "nozzle width". By the way please update what kind of printer you have in your profile - it's perfectly okay for you to not have any ultimakers as long as we are discussing Cura.
For example if you set nozzle width to ".4" and shell width to ".8" then the red line shown above will be .2mm in from the inner and outer edges just as one would want. You can verify this easily by looking at the gcode for a simple 10mm cube. This .4mm value would also be used for the spacing between inner shells, the spacing between diagonal infill and it would be used for the calculation of the amount of filament to extrude.
HOWERVER, I'm sure you *are* still seeing vertical holes smaller than desired. Especially small holes for screws and if you have a square hold the edges are fine but the corners get cut off quite a bit. This is in the nature of PLA. When PLA is extruded at over 200C it very quickly cools - in milliseconds. When printing say a 3mm vertical screw hole it places it over the layer below but it's stretchy as it cools (it shrinks as it cools) and becomes like a liquid rubber band pulling inward. As the nozzle traces the inside circle the rubber band property pulls the filament inward a bit - especially since the layer below has already been pulled inward a bit. This is the major factor for why small holes are much smaller than desired. For a 3mm vertical hole I typically print it at 3.4mm.
There are 2 other factors - overall shrinkage of the part from glass temp (about 60C) to room temp(about 20C). This is only 0.3% and almost too small to mention here. Also your cad software converts circles into polygons. If that polygon has say 10 sides those sides cut *inside* the circle such that the decagon is smaller than desired. If you have only 8 sides it's even worse. I recommend 10 sides as a good amount - or at least the minimum.
So what is the solution? If you have the original cad files then increase all those holes by about .5mm. If not consider printing with maybe ABS which has a much higher glass temp and has different properties.
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