Electrically controlled droplet-based labs-on-a-chip operate under the principles of electro-capillarity and dielectrophoresis. The microfluidic mechanics of manipulating electrified droplets are complex and not entirely understood. In this article, we analyse these operating principles, especially electrowetting on dielectric (a form of electro-capillarity) and dielectrophoresis, under a unified framework of droplet electrohydrodynamics. We differentiate them by their electric origins and their energy transduction mechanisms. Our study shows that both electrowetting on dielectric and dielectrophoresis are effective for droplet generation and manipulation. In addition, our study demonstrates: (1) the presence of a wetting contribution to dielectrophoresis; and (2) contact angle reduction is merely an observable consequence of, not a condition for, the occurrence of electrowetting on dielectric. Simulations are used extensively in this article to illustrate device operation, to expose underlying physics, and to validate our conclusions. Simulations of electrically driven droplet generation, droplet translocation, droplet fusion, and droplet fission are presented.