I am not sure, but i believe you may be confusing a DS with a 2DS. Apologies in advance if I am assuming incorrectly.
The 2DS actually came out after the 3DS, and I think it will play almost all 3DS games. The DS was the previous generation while the 2DS is a simplified 3DS - no 3D and it does not fold.
See Superkid's post above for a link comparing them.