Any celestial body can vary in its basic properties by considerable amounts that would have a proportionally considerable effect on a wide variety of conditions on the moon and those that live there. But if your question is "what is the only difference that would be apparent between an Earth-sized body in free solar orbit and one in a lunar orbit?" then we can restrict ourselves to just a few.
They would bleed less profusely.
Nothing No One Can Hit A Planet
If a dwarf star crashed into a planet,the planet would likely explode.
It is giant. If it was small, it would be a dwarf planet instead of a planet.
The person would eventually die if they received a water transfusion instead of a blood transfusion. It would most likely be a slow and painful death.
At that distance, there would be no planet - just vaporised gasses.
we would all die.
A large gas planet like Saturn would probably not last as an inner planet - the sun would probably pull Saturn into it and destroy it.
The object would crash into the planet.
the planet will shake
It's days would be shorter
We all die