Converter powers 12 volt stuff when you are connected to shore or generator power, It also charges batteries. On the fuse/breaker box door is a model number, Please post it so we can rate your converter.
INVERTER takes power from the batteries and uses it to power it's loads.
IF I were designing a house system I might well decide to have the electronics powered full time by the inverter and put in a converter large enough to provide power to that as well.. (There is a reason for this) Years ago I visited an electronics store and they had what was called a power conditioner, You could put a truly scarey waveform into it, vary the voltage all over the place, Nasty spikes, Square waves, whatever you wanted to do, and what came out was some of the sweetest looking sine waves I ever saw on a scope display.
The unit had 3 major components
Converter----Battery---True Sine wave Inverter.
And that is the system I just described where the house inverter always provides TV power.
