The New York Strip is a cut of steak originating in the Loin Primal of the cow. Other names for the New York Strip include Kansas City Steak, Strip Loin Steak, Shell Steak, and Club Steak.
The Ribeye steak is a cut originating from the Rib Primal of the cow. The Rib Primal is further broken down into a bone-in Ribeye roast, which can then be broken down into bone-in (or boneless) steaks.
The New York Strip is perfect for grilling and marinating. Comparatively, the Ribeye steak really shines with pan searing. While both can be cooked sous vide, the Strip is better suited.
Generally, New York Strips tend to be the cheaper of the two steaks. At a steakhouse in NYC, a New York Strip will start around $35 for a 16oz steak, while a Ribeye can begin around $40 for the same size.