Not sure. They may still be cartridges, but they're thinner than GBA carts, so they might possibly be discs. I have a feeling its cartridges.
You also forget that the N64 used cartridges. Cartridges doesn't mean bad graphics, it just means less space. :P
But then again, with the way technology is advancing, I don't doubt that cartridges now might have a lot more room than cartridges in the days of the N64.
Whatever the DS uses, the DS games on on the top, kind of like the original Game Boy Advance's game slot. The slot you plug in GB(/C/A) games is on the bottom of the DS, kind of like where you plug in games on the SP. Apparently the seperate slots is because, unlike the GBA compared to the GB(/C), the DS cartridges or discs aren't in the same pin format as the old cartridges.