In conventional flow notation, the motion of charge flow is shown according to the (technically incorrect) labels of + and -. This way the labels make sense, but the direction of charge flow is incorrect. In electron flow notation, the actual motion of electrons is shown in the circuit, but the + and - labels seem backward. Does it matter, really, how we designate charge flow in a circuit? Not really, so long as we’re consistent in the use of our symbols. You may follow an imagined direction of current (conventional flow) or the actual (electron flow) with equal success insofar as circuit analysis is concerned. Concepts of voltage, current, resistance, continuity, and even mathematical treatments such as Ohm’s Law and Kirchhoff’s Laws remain just as valid with either style of notation.
Conventional flow notation is followed by most electrical engineers, and illustrated in most engineering textbooks. Electron flow is most often seen in introductory textbooks and in the writings of professional scientists, especially solid-state physicists who are concerned with the actual motion of electrons in substances. These preferences are cultural, in the sense that certain groups of people have found it advantageous to envision electric current motion in certain ways. Being that most analyses of electric circuits do not depend on a technically accurate depiction of charge flow, the choice between conventional flow notation and electron flow notation is arbitrary . . . almost.
Many electrical devices tolerate real currents of either direction with no difference in operation. Incandescent lamps (the type utilizing a thin metal filament that glows white-hot with sufficient current), for example, produce light with equal efficiency regardless of current direction. They even function well on alternating current (AC), where the direction changes rapidly over time. Conductors and switches operate irrespective of current direction, as well. The technical term for this irrelevance of charge flow is nonpolarization. We could say then, that incandescent lamps, switches, and wires are nonpolarized components. Conversely, any device that functions differently on currents of different direction would be called a polarized device.
There are many polarized devices used in electric circuits; most of them are made of so-called semiconductor substances. Like switches, lamps, and batteries, each of these devices is represented in a schematic diagram by a unique symbol. As one might guess, polarized device symbols typically contain an arrow within them, somewhere, to designate a preferred or exclusive direction of current. This is where the competing notations of conventional and electron flow really matter. Because engineers from long ago have settled on conventional flow as their cultural "standard" notation, and because engineers are the same people who invent electrical devices and the symbols representing them, the arrows used in these devices’ symbols all point in the direction of conventional flow, not electron flow. That is to say, all of these devices’ symbols have arrow marks that point against the actual flow of electrons through them.
Perhaps the best example of a polarized device is the diode. A diode is a one-way valve for electric current, analogous to a check valve for those familiar with plumbing and hydraulic systems. Ideally, a diode provides unimpeded flow for current in one direction (little or no resistance), but prevents flow in the other direction (infinite resistance).
Both "conventional" and "electron" models will produce accurate results if used consistently, and they are equally correct insofar as they are tools that help us to understand and analyze electric circuits. However, in the context of electrical engineering, conventional current is far more common. Thus anyone who intends to study electronics in an academic or professional environment should learn to naturally think about electric current as something that flows from higher voltage to lower voltage.
Converting energy to motion for more than half a century
It's actually a teensy bit more complicated than even that. The ICs that make up the processing electronics in the computers we're all using are modeled with both electron AND "hole" movements with differing characteristics, where "hole" is the vacancy in the atomic shells of the atoms involved in the semiconductor behavior. Holes are typically "minority" carriers in n-channel MOSFETs and BJTs, but are "majority" carriers in p-channel MOSFETs and BJTs. Bipolar junction transistor (BJT) models make use of hole injection into the base region to cause majority carrier (electron) flow in the collector
