On-grid is the default for city homes: panels + inverter tied to the grid, net metering, no batteries. Cheapest per kW, best payback - but it shuts off during a power cut (by design, for lineman safety).
Off-grid means batteries carry your whole load with no grid at all. It's for farms and remote sites, and it's the most expensive way to run a house that already has a connection.
Hybrid sits between: grid-tied with a battery, so critical loads ride through cuts and solar self-use rises. Pick on-grid if your supply is stable, hybrid if cuts are a daily reality, and off-grid only when the grid genuinely isn't an option.