Yup. You need lug nuts with a ball-shaped seating area for stock wheels (all years), and lug nuts with a tapered/conical-shaped seating area for aftermarket wheels.
There are two different OEM lug nuts that were supplied with the NSX. The '91-96 came with lug nuts with a black finish (part number 90304-SA7-811), and the '97-05 came with lut nuts with a chrome finish (part number 90304-SA5-013). The only difference is the finish, so they are interchangeable. Of course, both have the ball-shaped seating area you need for stock wheels. They're typically around $7 list, $5 discounted.
You can also probably find chrome-finished aftermarket lug nuts at your local auto parts store that have the ball-shaped seating area you need. Tuner lug nuts they have on the shelf will almost certainly have the tapered/conical seating area, but the ones they have behind the counter should have the ball-shaped seating area. (Check the seating area when you buy them.) They will probably have them in stock, since there's nothing specific about the NSX lug nuts (the chrome ones are the same part number as lug nuts for various other Honda/Acura cars). (In my experience at Autozone they might have 4-5 in stock and not always the 20 you'll need for complete set, which they might have to order.) Expect to pay $2-4 each at the auto parts store.