Shear force refers to the force which is acting along on a surface. Fundamentally, the force builds no inclination or angle to the surface on which it is acting. Within a beam, the shear force at any section is particularly the algebraic sum of the lateral forces acting on either side of the section.
For instance, have a look at the following image:
On the contrary, the bending moment addresses to the internal rotational moments that cause a section to bend. In the case of a beam, it can be measured as the algebraic sum of the moments about the section of all forces acting on either side of the section, where a sagging moment will make the beam concave (positive) upwards at that section, and vice versa for a hogging moment (i.e. negative).
For instance, have a look at the following image:
Now take a look at the detailed explanation of these two important sections: