I agree with BobM3
There are two types of RV connections. The 30 amp is supposed to be 30 amps at 120 volt. with 3 wires, hot 120 volt, neutral and ground. The 50 amp is supposed to be two 50 amp 120 volt using two 120 volt hot leads, a neutral, and a ground.
Someone could have wired the 30 amp RV with two hots and a ground with 240 between the hots. When you plug it in to a conventional outlet, you get 120 volts. The 50 amp receptacle could have been wired with both 120 volt lines off the same leg, so they are 120 volt to neutral, but would be 0 volts between each other, or wired of different legs, which would be 120 to neutral, but 240 between lines.
The only way I see you getting 120 and 110 volts and having had it run is if it is 50 amp connection, with one leg pulled down to 110 volts BEFORE you try and start the compressor. You would have 230 volts between the two lines before starting the compressor. Normally 230 volts would be fine- but if one leg is already pulled down to 110- what does it go down to with the compressor starting/running? As the volts go down, the amps go up, and the motor overheats.