AC is always alternating. That is the definition of AC. The sign changes periodically.
DC is always direct. That is the definition of DC. The sign does not change.
Regarding the current flowing in either an AC or DC circuit. It is certainly NOT random, but depends upon the connected load. As the load demand increases, the amount of current increases.
Your house is powered by AC currents. If you switch on a lamp, AC current will flow through the lamp. If you switch on another lamp, the load has doubled, so you will draw double the current. The magnitude of the current is not random, it is due to the number of lamps and appliances (the load) that you have switched on. The more you switch on, the more current is flowing, the more energy you use, and the higher your electricity bill!
Now imagine that your house was powered by a battery that supplied DC current. Exactly the same thing would happen. As you switched on more lamps, more current would flow from the battery. Again it is not random. The current VARIES as the load increases or decreases.
Simply if the current is VARYING then the magnitude (size) of the current is changing
if the current is ALTERNATING the sign of the current is changing.
Do not get hung up on the exceptions to theses rules. They are just confusing you and not helpful at all.