If you've added your website to Ahrefs' Dashboard, you'll be able to see the number of referring domains you have:

However, when you click through to Site Explorer, you'll see that the number of referring domains is different:

Why?

Dashboard

The numbers on your Dashboard is taken from our Live Index. However, note that these numbers are not real-time, and they are only updated once a day. 

Site Explorer Overview

The numbers on Site Explorer > Overview is also taken from the Live Index. These numbers are the latest value, which you can also see if you visit the Referring Domains report:

Related

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