Inverter is what changes 12VDC to 120VAC to power 120V appliances. Bigger inverters connected to bigger batteries can power bigger stuf. I hook small inverter to truck
battery, run 120V extension cord back to laptop to power it. Truck
battery recharges when I use truck.
I keep small inverter in glove compartment of truck to power laptop, cell phone, recharge drill, etc.
Converter, usually found in RVs, is aka a 12VDC power supply, changing 120VAC to 12VDC. When connected to shore power or
generator, it provides 12VDC to your 12V appliances. As a second function, it will also charge your
battery, but may do a very poor job of it unless fitted with a good smart-charging card. Without shore power or
generator, converter is useless.
I personally am never hooked up to shore power to justify the
weight of carrying my old, heavy transformer-based converter, so I pitched it (done that twice now) and bought a good battery charger (just once, moved it from old trailer to new) and use that to recharge when shore power is available. I probably wouldn't pitch a newer electronic converter, but I wouldn't spend anything to replace it. You can buy several good battery chargers for the price of one good converter and it's useful elsewhere, like charging neighbor's battery - YMMV!