I think you have a JIS compatible frameset. There should be about 0.1mm interference fit between the cups and the head tube. If your frame is 80s Japanese, this reinforces this assessment. But you need precise measurements of the headtube, the cups, the crown race, and the fork steerer.

Don't assume that what it says on the headset box matches what is actually in the box. Assume that the parts in the box are a jumble of mismatched take-offs from a old upgrade.

Finally, don't assume that Internet sellers or local shops know anything more than you do about this.

And the internet seller is simply confused: headsets never come with both crown races.