This link shows the extra requirements for strong law of action and reaction. Why is Newton's third law known as weak law of action and reaction? Is the strong law of action and reaction not Newton's third law? But while working with central forces we apply Newton's third law (which is known as weak law) and not specifically strong law of action and reaction. At least I never heard people saying like "from the strong law of action and reaction the two forces are equal and opposite", they say "from Newton's third law..." . Why is it not something like "there are two categories under Newton's third law- weak law and strong law"? What is the difference?
Not all forces are central. For example the Lorentz force is not a central force.
However I suspect most of us would regard the distinction between the weak and strong versions of the third law as rather pointless. The third law is a statement that momentum is conserved, which is itself the result of a fundamental symmetry. Whether the force is central or not makes no difference to this fundamental principle. I would file this one in the some physicists have too much free time category.
Why is it not something like "there are two categories under Newton's third law- weak law and strong law"?
Yes. There are two categories namely - the strong form and the weak form of Newton's Third Law.
What is the difference?
I quote from the following wikipedia link Classical Mechanics that
Newton's third law can sometimes be used to deduce the forces acting on a particle: if it is known that particle A exerts a force F on another particle B, it follows that B must exert an equal and opposite reaction force, −F, on A. The strong form of Newton's third law requires that F and −F act along the line connecting A and B, while the weak form does not. Illustrations of the weak form of Newton's third law are often found for magnetic forces.
I had come to know of this strong form of Newton's third law when my professor introduced me to this form while proving that the net force acting on a multi particle system is the external force acting on the system. He used the strong form to illustrate that all the internal forces cancel out as pairs of forces(like dipoles) act along parallel or same lines in opposite directions .