The left is default cube with one half removed using a Boolean Modifier. The right one I got using a second default cube and moving the bottom 4 vertices up a meter/unit. Both seem to have the "same" origin. Still, when using ProWood, the two give different results.
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If you changed the scale on a cube in edit mode you should apply the scale with Ctrl+A https://blender.stackexchange.com/questions/7298/why-is-it-important-to-apply-transformation-to-an-objects-data – Jun 15 '17 at 15:07
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Is that possible? I mean, "Moving", as I said, or scaling vertices in edit mode, so that the object's scale is changed? – Jun 15 '17 at 19:09
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2If you scaled in edit mode your scale shouldn't have changed, scaling in object mode would. – Jun 15 '17 at 19:26
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In your image it looks like the texture mapping is created on the mesh prior to changes made by modifiers (whether it is generate or UV or whatever doesn't matter here). This is causing the texture to appear to be split in half on the one with the boolean.
If you clicked apply on the boolean modifier they should look the same.
Sazerac
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Applying the modifier indeed makes the left look like the right. But is there also a simple way to make the right look like the left then? – Jun 15 '17 at 06:44
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1@marcus that way around is more complex. You could add a mapping node between the texture and the texture coordinates node, and play with the Z-scale and Z-position values until you get the same look. – Sazerac Jun 15 '17 at 06:54

