The Inverters can be categorized by wave form into:
Step wave inverter
Instead of the sine wave delivered by an electric utility, this inverter produces a square wave. Because current is a switched, or turned on and off, the generated current had very abrupt changes and over time looks like a wave with square corners
Modified Waveform inverter:

The shortcomings of the square-wave inverter become most evident when you try to use it to run a motor. Ac induction motors draw a substantial current surge on startup. They really prefer sine-waves to square-waves and may overheat on the latter. AC induction motors also store energy during a portion of each cycle, which will create problems if not returned to the battery or otherwise controlled.
Pure sine wave inverter
A few true sine wave inverters have appeared on the market, This kind of inverter will run motors cooler and may offer less interference with radio and TV. However, they are inherently more complex and less efficient, so they may not be justified in many installations.
It can also be categorized by application into:

  • Isolation inverter (which is supposed to be used in a isolated place which have no AC power supply. The inverter simply convert the DC voltage sourced from the battery or solar panels to the AC voltage).
  • Grid inverter( The inverter not only convert the DC voltage to AC, it also distribute the AC power into the utility power grid, meanwhile, the inverter can get the AC power from the grid to charge the batteries. It is more common that in this application, the inverter is being installed with a solar panel system nowadays).