If the femoral nerve is cut, then the muscles supplied by the femoral nerve—the quadriceps—will be completely paralyzed. Conversely, if the L4 root is damaged then the femoral nerve still gets a contribution from L2 and L3 so the quadriceps will not be paralyzed but will be weak. In addition, with femoral nerve damage you want to think about the peripheral nerve map, but with a compromised root you want to think about the dermatome map. On the other hand, if you cut a peripheral nerve then the muscles innervated by that nerve will exhibit complete flaccid paralysis. Note that in the case of a muscle that is innervated by two nerves (not common), that the second nerve can send a signal to the muscle. Take cutting L4 as an example, then there will be weakness of several different muscle groups but not complete paralysis. This is because L4 fibers make their way into several different nerves.