Difference between a joint probability and the probability of an intersection
Yes, they mean precisely the same thing.
Why different notations? Well, this is not the only place in mathematics where there are multiple notations. For example, $A'$, $A^c$, and $\bar{A}$ are all used for the complement of $A$.
The version with the commas is more compact, particularly since the other version should really read $\Pr((X=x)\cap (Y=y))$. Think of the trees saved.
The version $\Pr((X=x)\cap (Y=y))$ emphasizes the logical structure, so has some pedagogical advantages.