Blender is an art program.
The engine is not.
Vertex deformation (positioning) has limits.
The limits are very high on artistic programs where high fidelity is a must, and really low on game engines where fidelity doesnt much matter.
In easier words, you are comparing apples to oranges by the way of apricots.
Simply: don’t expect the two to match - ever.
Look similar? Sure, to some extent.
The bigger the object, the more likely it will look and shift the same.
That’s likely also the same reason for your unreal UVs having a black bleed.
You can correct that one by increasing the UV fidelity on the mesh though.
There isnt a fix for the accuracy of how a morph target pushes verts around. It comes down to math.
Also, further from the origin of the world, worse the error will be.