Can someone explain the difference between $\displaystyle \iint f(x,y) \, dx\wedge dy$ and $\displaystyle \iint f(x,y) \, dx \, dy$?

In general, is $\displaystyle \iint\limits_{D} f(x,y) \, dx \, dy = \iint\limits_{D} f(x,y) \, dy \, dx = \iint\limits_{D} f(x,y) \, dx\wedge dy$?

Does Fubini's Theorem disregard orientation, instead working solely with a measure space without assuming additional structure?

I've been trying to figure this out, and now I have a headache from trying to read stuff about it because it uses some weird physics prefix notation.

Any help is greatly appreciated. Thank you.