The Xbox Series S has 512GB of internal storage, while the Series X has 1TB (real storage is lower, as some is reserved for the system). Both consoles use the same blazing fast SSD, developed specifically for Microsoft's console.
However, you'll likely find that you fill up the drive in no time, even on the beefier 1TB, since so many modern games have large storage footprints.
On the PS5, it's easy to expand the storage. You can even add an M.2 SSD to your PS5. On the Xbox, it's a different story. You have to use the proprietary Seagate expansion card. While you can use other external storage for older games, those optimized for the Xbox Series S/X must use Seagate's device.
Though Microsoft says other manufacturers will have their own versions eventually, it hasn't happened yet, which means you're stuck with the expensive Seagate SSD.