Most experiments impose a potential on the working electrode and measure the resulting current. A potentiostatic experiment imposes a constant potential on the working electrode for a specific time period. The measured current is plotted verses time.

For potentiodynamic experiments, the applied potential is increased with time while the current is constantly monitored. The current (or current density) is plotted verses the potential. After the potential is scanned to a predetermined current density or potential, the potential scan may be reversed while the current continues to be measured. A potentiodynamic scan like this is referred to as reverse polarization or cyclic polarization.

Please read this article whose title is "Comparison Between Potentiodynamic and Potentiostatic Tests for Pitting Potential Measurement of Duplex Stainless Steels"

Most experiments impose a potential on the working electrode and measure the resulting current. A potentiostatic experiment imposes a constant potential on the working electrode for a specific time period. The measured current is plotted verses time.

For potentiodynamic experiments, the applied potential is increased with time while the current is constantly monitored. The current (or current density) is plotted verses the potential. After the potential is scanned to a predetermined current density or potential, the potential scan may be reversed while the current continues to be measured. A potentiodynamic scan like this is referred to as reverse polarization or cyclic polarization.

I agree with Dr. Fahamsyah's answer.

Dr. Fahamsyah is right :) simple terms !! 

Sorry I think I am only seeing this for the first time, but i would suggest otherwise in some aspect.In Dr. Fahamsyah's answer he suggested that "a potentiostatic experiment imposes a constant potential on the working electrode for a specific time period. The measured current is plotted verses time."

My additional answer:

These are the two main divisions of interfacial electrochemical techniques. In the potentiostatic technique (ideally) we do not allow current to pass through the analyte’s solution. However, current may vary, but very small which accounts for the logarithmic scale used. Thus, we measure the potential of an electrochemical cell under static current conditions. The plotted quantities are potential verses time or potential verses logarithmic current.  The difference between them I suppose is that in static (current, I ≈0) while in dynamic (current, I ≠ 0).

I think you need to know the difference in corrosion calculations, the first test which is the potentiostatic test in which when you imposes a constant potential on the working electrode for a specific time period, the measured current is plotted verses time. In Titanium for example, you need to know the stability range of titanium oxide layer that can prevent the pitting corrosion with time, so the resulted curve give you an indication about the oxide layer stability, every increase or decrease in current over time it gives a sign of pitting corrosion and it refers to a penetration in the oxide protecting layer and a flow of a current through which. on the other hand the potentiodynamic test will give the Tafel data Icorr and Ecorr and the corrosion rate (will be given by the software), which is the required value because in the end you need to know how much material will be eroded.

Potentiostatic means constant applied voltage with variable current with time (plot I vs. time). Potentiodynamic variable potential and current (plot E vs I)