Not quite.
The power company sends those electrons out over three wires which are 120 degrees out of phase. Those wires travel great distances to the cities where the power is needed. A fourth ground wire also travels the same distance from the generating station to the city it services.

Once the wires get to the cities, then depending on the zoning in the city (whether, industrial, commercial or residential) the power from those wires is distributed differently. Industrial areas that need three phase power for their big three phase electric motors will be serviced by all three wires. Commercial and Residential areas will only be serviced by one of the three wires. At each telephone pole distribution transformer there is a step down transformer with a center tap that converts the 7200 volts carried in the one of those wires down to two 120 VAC wires, each 180 degrees out of phase with each other, and a neutral wire coming off the center tap of the transformer, as shown in this diagram:

http://tinyurl.com/ly24tjo