Normal Solar Inverter：

Normal Solar Inverter, we mostly refer to on grid inverter or grid-tied inverter. The basic function of a solar PV inverter is to convert the DC electricity generated by solar panels into AC electricity, suitable for injecting into an electrical power grid

Hybrid Inverter：

Hybrid Inverter=  Normal solar inverter+  battery inverter. In the context of residential solar+storage systems, a hybrid inverter (sometimes referred to as a multi-mode inverter) is an inverter which can simultaneously manage inputs from both solar panels and a battery bank, charging batteries with either solar panels or the electricity grid (depending on which is more economical or preferred).  

The hybrid inverter works by storing surplus energy in batteries for later use, making it possible to utilise solar power time-independently by storing unused capacity, or to save cost during peak electricity rate.

The solar hybrid inverter will first use the solar power, if the demand exceeds the solar power it will supplement it with mains utility power. If the solar power exceeds the power demand the excess power is used to charge batteries. If the batteries are fully charged the excess power can be fed back into the grid. 

So the most big difference is hybrid inverter with battery energy storage system.