Many nurseries decline to change rose names despite being told they're incorrect. They don't see it as unethical. They don't think adequate research has been done to justify changing, or they trust the supplier, or they assume the breeder's descendants will have the correct rose, or international experts grow it by that name, or that's what it's labelled in Sangerhausen (though it has been through two world wars), or that's the name they've always grown it under, or it's the name the public know and ask for it by.
It's exasperating.

What are the differences of Heirloom's rose?

You're welcome! I'm glad I could help clear that up for you. Mr. Moore theorized that the mauve petal base of Anytime was an adulterated red. He bred Anytime with Angel Face to intensify and enlarge the mauve base then began crossing with others to reduce the "blue", intensify the red and fix that trait as more likely to be gained through breeding. That required a bit of self crossing, and it worked! The most "Hulthemia-like" was Halo Sunrise which contains the cross of Anytime X Angel Face three times with two doses of Gold Badge to pick up the yellow.

ARS states that the blooms have a diameter of 4-5 cm. Someone must have mixed up centimeters and inches. On photos with foliage, the blooms do seem smaller than 10 cm. Someone who grows this rose might have first-hand experience.