Plane stress or plane strain hypothesis are approximations linked to the supposed form of stress and strain tensors i.e. we suppose the out of plane stress or strain component is small compared to the inplane ones and we neglect it. This is usually linked to the geometrical characteristics and not to the constitutive relations between stress and strain.
Sometimes, in FEM software, you can choose between plane stress or plane strain hypothesis in a 2D model. This is usually linked to the direction "out of the screen". The one you have to choose is linked to the width of the "beam" (a beam is usually a 1D element, not a 2D one): plane strain should be used for wide beams.