“Why is there ‘single-phase’ and ‘three-phase’ power, but the commonly available 120/240VAC is not called ‘two-phase’?”

It has to do with the sorts of power available from electrical utilities and how it gets to you. Electrical utilities generate and transmit high voltage three-phase power throughout their distribution network, from huge transmission towers down to utility poles, because three-phase power is required to run the powerful motors used by industrial and commercial equipment. Most industrial, commercial, and theatrical buildings are equipped with three-phase power.

Hanging three-phase power on every utility pole everywhere is expensive, and for electrical customers (such as homes) who do not have large motors, just one phase is required, so the electrical utilities provide just one of the three phases to the customer, hence the term "single-phase".
For homes and small offices, the power company supplies that single-phase through a transformer. The transformer is required to reduce the high voltage down to what is required to run common appliances. However, some appliances like electric ranges and washing machines need more power and operate at 240 volts, while electric lights and computers need less power and operate at 120 volts. To provide both voltages, the transformer's output is "tapped" and grounded in the middle, providing both 240 volts (the transformer's main output) and 120 volts (between one of the transformer's outputs and the tap).

Even though there are two voltages available, this is called "split-phase" and not "two-phase" because it is still being derived from a single power-company phase. On a more technical level, the 120V and 240V available from a split-phase service will have no phase-offset in the way that three-phase sources do (and three-phase motors require), so it's still a single, and not two, or three phases.