Domain Rating vs URL Rating
Ahrefs has two main authority scores. Domain Rating (DR) measures the link strength of the whole website. URL Rating (UR) measures the strength of one specific page. A strong site can have weak pages, and a weak site can have one page that went viral. When you are judging whether a website is worth a link, DR is the number to start with. When you are judging a specific page, look at UR.
Domain Rating vs Domain Authority
Domain Authority (DA) is a similar metric from Moz. Both use a 0–100 scale and both are based on links, but they use different link indexes and formulas, so the numbers rarely match. A site might be DR 45 and DA 32. Neither is “right”; they are two opinions from two tools. Many link sellers quote whichever is higher, so always check the one you use yourself.
Why DR is popular with link builders
Ahrefs has one of the largest link indexes and updates it quickly. DR also reacts relatively fast to link manipulation being removed, which makes it harder to fake than some older metrics. That is why most link marketplaces and guest post lists show Ahrefs DR as the main number.