Zero crossing optocoupler

What is the difference of the optoisolators having zero-crossing feature (MOC3021) and non zero crossing feature (MOC3041)? What are their application fields?

The zero-crossing feature is useful to prevent the RF interference that is generated when an alternating waveform is switched on at a non-zero part of the cycle (that is, most of the time). However, it will wait for that zero-crossing which can give a small delay (up to half the period) and obviously cannot be used for phase-angle control (as in the classic light dimmer circuit).

The non-zero-crossing part will switch on as soon as the signal is applied. If current is drawn suddenly because the cycle is part way through, then RF interference will be generated. It is useful though when the angle must be controlled, switching must be instant, or DC needs to be switched (since DC won't have a zero-crossing to detect).

By the way, you got the parts the wrong way around.

Could you please refer a timing diagram of both?

You will find them in the datasheets for the two devices.