The plastic modulus of asection is a value that multiplied by Fy gives the plastic Moment capacity (Mp) of the SECTION. It is a geometrical property. The value you quote is for rectangular sections, not double tee. See p. 68 and following of the following reference
where it is seen that for a relatively thin wall pipe the plastic modulus of section is 1.27 times the elastic modulus of section.
It is a geometrical property. Mp respect a line parallel to some line is a line parallel line that divides the section in two equal areas, all loaded at Fy, so the way of getting Mp is dividing the area in two equal parts and making one work at Fy in compression and the other at Fy in tension. Multiplying such C (or T) by the arm between centers of gravity of the respective (halved) sections gives Mp. Divide by Fy and you get your plastic section modulus.
So since Fy is eliminated on the division of Mp the plastic modulus is just a property of the section.
For a rectangular section
Mp=C·arm=Fy·Acomp·arm=Fy·(b·h/2)·(h/2)=Fy·Z=Fy·b·h^2/4
Z=b·h^2/4 the plastic modulus.
Since the elastic modulus of section is b·h^2/6 you can extoll 1.5 times more strength of the structure if allowed (and can) go to a plastic section behaviour. For a pipe section, that would be 1.27 times.
That is the plastic modulus of a section. Then the Shear Modulus of a Material is entirely another different thing, it is a material property in theory of elasticity akin to what the Young modulus represents for axial deformation, but for shear action... Is someone misleading you? If you can precise your question we may also write a little about the shear modulus.