Inverters are type of converters, which DC voltage are converting into AC voltage.
According to source of DC voltage inverters can share in two groups:

The source of DC voltage is battery. Inverter convert the battery voltage into regulated AC voltage with stable value and frequency. Wave form of voltage napona may be sine or similar to square (commercial terms: modified sine, trapeze and alike.). Sine inverters are suitable for supplying all type of loads, but they are more expensive than "square".

Solar modules are directly connected on input of these inverters , and on output public electric grid. DC voltage of modules converts to AC, where there is sinhronization with grid voltage. Battery is not necessary. The flow of electric energy is always from modules to electric grid.

Chargers are type of converters which AC voltage converts to DC voltage. If their main purpose is charging the batteries than they are called chargers.

Combi devices are special type of converters which can work in two modes: as a inverter and supplying the loads (when there is enough energy in battery), and as charger(when the battery is empty). On combi device you can connect agregate or some other source of electric voltage(for exa. grid). With build in transfer switch, energy from agregate is automatically taken to inverter, which from alternating mode, also automatically, transfers to charger mode and is charging the battery.