I wonder whether alternating current is produced from DC current or whether AC and DC are entirely different concepts. Is there any relationship between AC and DC?
AC can be made from DC, and vice versa. DC is a steady voltage, with AC the voltage fluctuates from negative to positive and back, many times per second.
Most electricity generators generate AC. The reason for preferring AC is that, historically, it is easier change voltage with AC: all you need is a transformer. The generators generate a high voltage, although usually a transformer is used to get it even higher.
The reason for the high voltage is to reduce losses in the cables (at higher voltages less current is needed for the same power, and less current means less heat waste). This high voltage gets sent down the powerline to a substation, where a transformer converts it to the 240V (110V in the US) used in the home. Most electronic equipment requires low voltage DC to operate. Converting AC to DC is easy. In essence, all you need is a rectifier - just a diode will do, although you probably need a transformer first, to reduce the voltage down further. In practice more complex circuitry is used to make sure the DC is smooth and stable.
Modern electronics make it fairly easy to convert DC back to AC. In fact, a normal powerpack (wall wart) first rectifies 50 Hz 240V AC to DC (at over 300V), then converts that to AC at several hundred kHz, and finally back to 5V DC, all within a small black cube.
To avoid AC losses in powerlines, some run DC instead of AC, at hundreds of thousands of volts. That kind of conversion is not exactly easy!