Come around to my place...

1. No.
2. Yes. You can also come over or come round.

Is there any difference between "come around" and "come over"?

Not that I know of. One might be more common in certain places, but in this context, I would use either one. I believe come round is BrE and come around is AmE.

In other contexts, to come (a)round can also mean to change your opinion so that you agree with someone else:

he disagreed at first, but in the end he came around

"come over" is more direct.

"come round" seems more haphazard. If you're out and about, why don't you come around my place.

Is "come over" more preferable if the dinner is planned previously?

To me, it's a more direct invitation.

Alex, would you like to have dinner with me and my family? You would? That's great. Why don't you come over about 5:30 and you can meet the kids.

You will certainly hear "Why don't you come round about 6 or so" but (again, to me) this seems more casual. You can come at 6. Or earlier. Or later.

Thank you, everybody, for your replies.