This question must be broken down into several parameters. The amount of current that can flow through the contactor continuously is determined by the heat dissipation capacity and the maximum continuous current is often referred to as Ith or thermal current. Often a higher current can be run for a shorter time.
When switching off or breaking under load, an arc is always created. The energy in the arc is determined by the current and voltage and the type of load being broken. The arc is ionized gas, s.k. plasma. The energy of the arc is very high and powerfully destructive for the e.g. the contacts. Depending on the design, the contactor can handle the arc in different ways. The aim is always to cool the energy in the arc to create a safe situation and reduce wear and tear. The breaking capacity is always given in amperes at a specific voltage and time constant of the load.
When switching under load, small arcs may form but these disappear as soon as the contact is closed. The capacity for switching is often much greater than for breaking and is given in amperes at a specific voltage and time constant for the load.