Amusingly, "crystal oscillator" can be both "X" and "Y" in schematics.

"X" because "xtal", and "Y" because of the distinct shape of a tuning fork.

Even more amusingly, only low-frequency crystals (very often 32.768kHz) are tuning-fork cut, high-frequency resonators use other shapes.

Pedantically most of them aren't crystal oscillators, merely crystal resonators. Oscillators begin oscillating on their own when a DC voltage is applied, they usually are 3-pin or 4-pin devices with power input & oscillating outputs. 2-pin crystal resonators merely act as high-Q filters in an oscillator circuit, they still need other components to drive the oscillation.