Hybrid PV inverter typically means that it's connected to the grid and can utilize battery storage.
Solar and grid (no battery): I just call it "grid tie". I have this.
No second meter. Back-feed the existing meter. Yes, POCOs may handle this differently and it shifts the economics. 1:1 "net meter" is a good deal. Payback at wholesale or less is per kWh is a bad deal.
Various ways to play the game if you have battery storage. You can set your inverters to discharge power during high cost-to-use periods, making sure you maximize your return by using less grid power. But yea, PV + inverter + battery ain't cheap.