How do we know an event is a gamma-ray burst? How do we know an event is a gamma-ray burst (grb)?

There are two kinds of grbs, long burst and shot burst, which are caused by supernova explosions explosion and the merger of two neutron stars, respectively. However, at least one grb, J1644, is a tidal disruption event. Is there any other grb which was not caused by a supernova or the merger of two neutron stars?

When can we say that a supernova explosion is a grb after observations? How do we know an event is a grb especially when we missed its explosion?

Can we tell that the afterglow is caused by a grb?

Please give me some reference papers since I am a layman of this field.
Yes, on the right track where the energy produced in a supernova can indicate if it was a LGRB or SGRB.

An indicative tools stems from the light curves of the remnants, both the afterglow brightness and it's region of explosion can indicatively be traced to how long the event lasted. Large gamma-ray remnants are typically associated with rapid star formation regions and are a more luminous remnant, where short gamma-rays are typically associated with little or no star formation regions and are a less luminous remnant.

It's not an exact science, as reproducing the effects and duplicating results have proven vastly difficult, however using distribution plots can definitively separate the differences and provide a theoretical model to work on.

Some minor information can be found at Wikipedia, however further reading and a more in depth view can be found at Cornel University Library. It is a bit of a read and attempts to explain the physics behind emission through mathematics, I'm not entirely sure whether is will provide the answer you are seeking.