Actually we don’t know if the power from your inverter is the same as “shore power”.
There’s more to it than just voltage and wattage. There’s also the A/C waveform, and it’s important.
The really good inverters produce “pure sine wave” A/C power, like what you get at home from the utilities.
If you looked at the A/C wave form on an oscilloscope you’d see each of the two wires roll smoothly from 0 volts up to 120 volts positive then smoothly back down to 0 and smoothly down to negative 120 volts, and back up again. The two wires do this opppsite of each other, so as one is rolling up to positive 120, the other is rolling down to negative 120. That smooth curve you’d see if you saw it on a scope is called a sine wave.
That’s why it’s called Alternating Current. Each wire alternates from positive to negative.
It does this 60 times per second. That’s what the 60Hz spec you may have seen means. (At least in the U.S. Some other parts of the world use a 50Hz standard.)
Cheaper inverters don’t roll the voltage smoothly up and down. They just switch it instantly all the way on one way, then all the way the on other way, abruptly.
That’s called a square wave, because if you look at it on a scope the wave pattern looks square.
Many electrical things don’t behave well on square-wave power. Some barely function at all.
There’s an in-between called “modified square wave” which is like a square wave but it steps the voltage halfway up then all the way up. It’s closer to a smooth sine wave but still really isn’t.
Whether your camper appliances (such as the battery charger) work the same on your inverter as they do on “shore power” depends on what type of inverter you have.
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