There are two different IDs you can get in NYS, the driver's license and non-driver photo ID. Both have the same paperwork requirements, except the non-driver you do not need to pass a driving test (duh).
The following is from New York State Department of Motor Vehicle's website:


"A person of any age who does not have a driver license can apply to the DMV for a non-driver photo ID card. You must provide acceptable proofs of identity and date of birth. You can apply for a non-driver photo ID card if your NYS driver license is suspended or revoked. When you apply for a non-driver photo ID card you must surrender your NYS driver license. There are no exceptions. You do not have to surrender a non-driver photo ID card when you get a driver license or your driver license is reinstated.

A non-driver photo ID card contains the same personal information, photo, signature and special protection against alteration and fraud as a photo driver license."