Honda Civic 14" rims - do I need different lug nuts?

I picked up some 2001 Honda Civic rims with studded snow tires over the weekend. I read here and other places that they would fit - and I tried one on the front and went lock to lock steering and they do fit. My question is about the lug nuts. They don't seem to tighten down the same way as on the stock Mirage rims. Where the nuts fetch up solidly at a certain point on the Mirage rims, the same nuts on the Civic rims seem to not fetch up. I also noticed some metal filings coming off the nut so I stopped pushing it. Do I need new nuts?

Take a close look at those wheels. Do they use they same style of lugnuts that the Mirage uses? There are 2 major types of lugnuts and they aren't interchangeable...

Attachment 9830

Yup, that's it. Thanks for the diagram. I need to order some nuts.

I understand the spherical type is common on Hondas.