As of January 1, 2014, New York switched to the new high school equivalency (HSE) test developed by McGraw Hill called the Test Assessing Secondary Completion, or TASC. It is computer based, although a paper-based test is available. You'll see reference to PBT (paper-based test). The state formerly offered the GED (General Educational Development) test from GED Testing Service.
Information on the New York State GED website isn't pretty, but it offers answers to many of your questions, including what happens to your old GED test scores. A heads up: the links require you to download Word documents.
Good luck! Come back and share your experience with others: Which Part of the GED Test Is Easiest/Hardest?