Difference Between Sine Signal Generator and AC Power Supply Functions and Uses

What is a difference between sine Signal Generator and AC power supply?

An AC power supply is designed to power something. A signal generator is typically designed to supply a signal, not necessarily to power something.

And as Colin pointed out, a signal generator is more likely to have an adjustable frequency -- and made adjustable more for facilitating other circuitry and less for matching some power requirement (at least, not directly).

Your eBay link describes a Signal Generator, not a Power Supply. It doesn't list it's driving capability [if it was an AC Power Supply, it would be silly not to included that], but judging by the included schematic, it won't be able to drive much (i.e. nothing like a typical Power Supply).

Thanks for answer.

An AC power supply is intended to supply power to AC powered electrical devices.
Examples:
120V or 250V electrical supply to buildings, accessed from wall sockets, supplying energy from a power station (which is itself a type of power supply unit).
A petrol or diesel engined generator, used to supply mains appliances away from a building.
An inverter, which may take its input from a 12V vehicle battery, and output 120V or 250V AC.

A Signal Generator is a device that produces a electrical waveform for testing electronic equipment, such as amplifiers.
Typically, the frequency, shape and amplitude of the output waveform can be varied.
Its output power is usually very low.