Hi John, flush mags fit, but the extended mags will only fit if you remove (or modify) the grip extensions.
The 7-round mags from the original XDs 45 will fit in the XDs Mod.2 if you remove the plastic magazine sleeve.
Stay safe & have a great day!

The Springfield Armory XD-S 45 ACP and the XD-S Mod 2 OSP 45 ACP have different magazine capacities and some magazines are not interchangeable between the two models:

XD-S 45 ACP
Comes with a five-round flush magazine and a seven-round extended magazine.

XD-S Mod 2 OSP 45 ACP
Comes with two stainless steel magazines: a seven-round magazine with a pinkie rest and a nine-round extended magazine.

Interchangeability
Flat floorplate magazines can be swapped between the two models, but extended magazines cannot. To make extended magazines fit, the floor plate can be removed and replaced with a mod to floor plate.

The XD-S's "S" stands for single-stack magazine, which provides a slimmer grip.

Hi John and welcome. Yes Sir, the magazines are cross compatible between the XD-S and XD-s Mod 2. Cheers, stay safe and enjoy!