Force distributes the total load to the nodes that are on the face selected.

Remote Force creates a single point at the centroid of the face to apply the total load, and generates connection elements from that point to the nodes on the selected face.

The very tiny side-sway is the numerical round-off error in the solution because the stiffness to sideways motion is orders of magnitude lower than the stiffness for stretching the part. Best to just add a constraint to prevent sideways motion that in a real test is provided by a massive testing machine.