The project tool shifts the output of the coordinate system.

[MohammedAlkherallah]

I share the project tool as a tool in ArcGIS Enterprise, then I use it in ArcGIS Web AppBuilder as geoprocessing. I see that when I use the tool, it shifts the layer, but in ArcGIS Pro, it doesn't shift. What is the problem?

in ArcGIS Pro: (no shift)

in ArcGIS Web AppBuilder: (shift)

[DanPatterson]

Pro uses the coordinate system of the first added layer.  Anything added subsequently is projected-on-the-fly to match it.  So depending on what you are adding and what its coordinate system is/was, you may or may not see a visual shift

[DavidPike]

Adding to what Dan has posted, the transformation used may also differ.