Actually, many frequencies at once. The square wave generates all of the odd harmonics of its base frequency up to the frequency limit of the device that is driving the square wave. For most 555 type devices, this is somewhere between 800 kHz and 2.0 MHz, depending on the actual device.
White noize is also present in the square wave to a limited extent, due to randomness in the circuitry.
The problem with pure white noise is that the frequencies that are specifically needed are diluted by all of the other frequencies that are present.