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The one on the left is for an aluminum wheel, the one on the right is for a steel wheel. If you have hubcaps over the lug nuts just plain wheel lug nuts are fine.
Replacing the rims on my 74. The old ones are damaged. I know it’s 7/16-20, but neither match up to the rim like they should.
is there a specific design I need?
What do you mean by match up? The tapered seat nut on the right should work.
Do you know the manufacturer of the wheel?
Is the hole in the center of the wheel the same size as the hub?
It appears that the wheel in the photo is a lug centric wheel. As MelWff stated, tapered seat nut should work. You'll need to jiggle the wheel around in order to center the wheel on the lugs, then tighten the nuts.
Not sure if you are aware or not of how important it is that you cross tighten these lug nuts. Get the wheel up in place and lightly tighten each nut, in a cross pattern. Then go around again, doing the same cross pattern. That is the only way to make sure it is centered. And as suggested, go over them again in a few days.