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Is it there any differences between a thermal relief in a 'X' shape for a '+' shape? I am using Altium and the software has boths styles for selection.

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It can make a difference if you have a lot of them packed together in an array, such as in a multipin connector. If the pins are close enough together that the copper "pour" between them disappears, it can leave the legs of the thermal "hanging", not connected to anything. Switching to the other orientation can mitigate that to some extent.

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If I recall correctly, the only difference is the orientation relative to the x-y axis of your PCB design. So the + style will be 0 degrees relative to the y axis, and the x style will be 45 degrees.
Electrically there is no difference.

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