Is there any difference?
I read somewhere said that "move aside" implies a little bit of ordering rather than asking. Is it true?
Mom was cooking dinner and her little daughter was blocking her way.
Mom: Can you move over/aside, please?
Yes, I believe both have similar meaning, but "move aside" is a little more formal and thus distant, and more often used when you are blocking the way and must make a significant movement. Like I can imagine a a police officer moving toward me say "move aside sir" or "step aside sir," than saying "move over sir."
https://idioms.thefreedictionary.com/move+over
To physically create space between oneself and someone or something else.
https://idioms.thefreedictionary.com/move+aside
To move to one side, especially to get out of someone or something's way.
"Move over" is more likely to be about moving to make space for someone to go into and stay there.
You move over to give someone room in the bed, for example, or to space at the worktop in the kitchen to cut the carrots.
"Move aside" is more usually about ceasing to block someone's path or line of vision.
It's also more usually used as an order rather than a polite request.
None of the above is absolute. You could certainly say any of the following options "Move/Shift/Shimmy aside/over there and let me through the door" with perfect joviality.
"Move over" tends to be cuddlier, though. It implies that some shoulder contact mightn't be a problem. In contrast, "Move aside" tends to imply a desire that the listener get right out of the way!