what is the difference between a sinusoidal current signal and an alternating current signal (ac) ?

Question

anonymous · Answer

There is no difference, except when you say "AC signal" you can talk about sine, square, saw or whatever type of signal. 
In other words sinusoidal signal IS AC signal, but there are many types of AC signals.

anonymous · Answer

but when we give the input to a device through a signal generator kit, there are two ports, one for sinusoidal and once for ac... usually we say that the current that is used for domestic purpose is ac with sinusoidal waveform with some frequency. but if ac is sinusoidal then what is the waveform of a sinusoidal signal then...

anonymous · Answer

It's a sine wave (waveform of the sinusoidal signal), if that's what you are asking.
Signal generators have a switch for you to choose which waveform you want, so I don't know why would one have one output for only sine wave and the other for general AC or whatever. Can you maybe provide a picture or something, or a model of the signal generator?