Hooke's Law vector form
If we sidestep your typo (the last term has one absolute too much), both formulations are correct. They just express different things. The $k$ in Hooke's law is for a particular spring. $k_s$ is the siffness for a paricular material. 

Now in the linear portion there is a direct relationship betwen these the material stffness is directly propotional to the spring factor and length of member. So for example when the rest length of a different spring with same material is 2 times as long its 1/2 as stiff.