Slope:
A simply supported beam when loaded will bend along the length of the beam. At the mid-span, the beam will have maximum deflection or depression measured from the original level surface. The ends of the beam resting on the supports will not remain horizontal but will undergo a change in the angle from the horizontal. This change in the direction of the bottom of the beam from the original horizontal is the slope.
Deflection:
When a structural is loaded may it be Beam or Slab, due to the effect of loads acting upon it bends from its initial position that is before the load was applied. It means the beam is deflected from its original position it is called Deflection,
and the slope of that deflection is the angle between the initial position and the deflected position.
Consider you are holding a somewhat flexible stick with your fingers, and tie a little weight on the free end with the help of thread. that means it has become a Cantilever with point load at its end. you will notice that the flexible stick will bend down due to the weight which is hanging at the end. You will also notice that the bending from its initial position is maximum at the free end and minimum at the point you are holding it. This is Deflection.
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