Static power is the circuit leakage power. Static power exists even if there is no activities. When power is applied to the transistors, transistors would leak current naturally due to physical characteristics of the silicon and manufacturing defects. Examples of static power include transistor drain to source leakage and silicon substrate leakage.
Dynamic power is the power used to charge or discharge transistor intrinsic capacitor. Dynamic power only exists when signals toggle either from low-to-high or high-to-low. For example, clock toggles every cycle, thus clock paths consumes huge amount of dynamic power if there is no clock gating.
Short-circuit dissipation power occurs when both NMOS and PMOS transistors are active for a small period of time, during which current will find a path directly from power rail to ground. Hence, this creates a short-circuit current. In first-order analysis, we assume 0 transistor rise / fall time during transition, and short-circuit dissipation power can be ignored. However, we shall assume finite transistor transition time in more accurate analysis, thus short-circuit dissipation power exists every time signal toggles.