What's the difference between Rotation speed vs takeoff speed? My aviation teacher told us to memorize some speed values among other things before our flight training:

$V_R$ = 40 kt
$V_S$ = 39 kt

According to wikipedia:

Vr:
The speed at which the pilot begins to apply control inputs to cause
the aircraft nose to pitch up, after which it will leave the ground.

But I'm somehow confused with the values, since the takeoff speed (according to what I was taught) should be 10-25% greater than Vs, in this case around 43 and 49 kt.
If Vr is the definition mentioned above, which should be takeoff speed? does it have a definition within V speeds? Isn't takeoff speed the speed at which the aircraft leaves the ground?
Thank you
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.