I would use the word foreshortening, which means to project the deflected shape onto the X axis. The projected length is shorter, but the physical length along the curve of the beam is actually a tiny bit longer.
The beam is a tiny bit longer because the angle between the beam axis and the force is no longer 90 degrees at large deflections. In the nonlinear graphic, it looks more like 135 degrees. In the element at the tip, the vertical force at 135 degrees to the beam axis can be decomposed into axial tension and bending moment. The tension makes the beam a tiny bit longer by an insignificant amount.
There is no net force along the X axis.
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