One is the inverter's continuous output rating. This is the maximum wattage the inverter can output on a long-term basis. The second rating is the inverter's surge capacity rating. This is the maximum wattage the inverter can output on a momentary basis. Surge capacity will often be 2x or more in excess of the continuous rating.
All appliances require more power to start than they use while running.
Many appliances, such as refrigerators and water pumps, will require up to three times as much power to start as they require while running. The combined starting power required by all inverter powered appliances must be within the inverter's surge capacity rating. If the inverter is only running certain loads in the system, those specific circuits will need to be wired to the inverter through a sub-panel. Different wiring layouts are used depending on whether the inverter is in a remote power system, a grid backup system or a grid intertie system. Many inverters include built-in battery charging functions, which is especially useful in grid backup systems.