[Supperman]

make a big deal

I heard that America is a litigious society.
I heard that when someone spilled a coffee of McDonald's and got burnt, he sued McDonald's, claiming that the coffee was too hot.
I would like to say, "hey, you should not make a big deal out of it. I'm not proud of yourself. It's quite a shame if I judge from the Bushido point of view!".
............................
Which is correct? Both?

Tomorrow is my birthday, and I'll have my birthday party tomorrow.
But don't tell other members, because I don't want to make a big deal out of it.
But don't tell other members, because I don't want to make a big thing out of it.

Is there any difference in meaning?

Thank you.