On-grid inverter contains Max Power Point Tracing (MPPT) module and inverter unit (DC-AC). Inverter always needs to trace the max power to generating power. Therefore, voltage, frequency and phase of AC Output should be the same as those of grid.
Off-grid inverter transmits power by energy storage device. Voltage and current are in a stable situation. Therefore, power of off-grid inverter is highly related to power and quality of load.
The technology of large power electronic elements is the foundation of development of modern inverter technology, because the key component of inverter is electronic elements.
PV inverter is developing to higher frequency and smaller size. Inverters without isolation transformer are the mainstream now. The most promising direction is micro-converter and mini-inverter (module inverter). Enphase, an English energy company, Microinverter, an US company, and Solarmagic technique of State Semiconductor of America draw attention of public.
Due to heterogeneous sunshine, diversity of PV module, complexity of installation, such as BIPV and tree shade on rural house, micro-inverter has a much wider market. Inverter will realize modularization and generate in a distributed pattern.
The difference between A and B, please see: 《What’s the difference between On-grid inverter and Off-grid inverter？》