Difference between pulse and blood pressure
The blood pressure is the fluid's movement "strength" in the
  arteries (or "artères", please edit my post with the correct english word)


Blood pressure is a measurement of the strength of flow through the arteries. (I.e., the force per unit area exerted by the blood on arterial walls.) So replace vein with artery and your definition is correct.


  The "tension" is the force applied on the veins itself, kind of like
  when you're pulling a rubber band


In cardiovascular terminology, hypertension and hypotension are used interchangeably with high and low blood pressure (even though technically tension uses force units and pressure uses force/unit area units). Your definition sounds more like arterial tensile strength, which is the ability of the artery to withstand pulling forces without breaking (which decreases with age).


  The pulse is just the wave of blood moving, which creates different
  tensions over the vein and whose movement is created by the pressure.


Pulse is an indirect measurement of heart rate. So, yes, it's the rate of the "wave of blood moving." It creates different "pressures" measured by systolic (the "wave" in your terms) and diastolic (the "trough") whose movement is created by the force (of the heart walls contracting).