What's the difference between Rotation speed vs takeoff speed?
Based on the speeds that you are talking about, it isn't a turbojet definition that you are looking for.  The definition for $V_R$ that you gave is for turbojets.

In small GA airplanes, I teach my students to rotate around $1.3V_{S0}$ which really means to slowly bring the nose up to the takeoff pitch attitude.  Under no circumstances do I want them to yank the airplane off the ground.  If done correctly, the airplane will naturally lift off when it is ready to.