The links tool calculates the total number of linking domains using data recorded from Moz when your account was first created, along with updated referral traffic from your sources report over time.
The competitors report uses updated linking domains data from Moz over time. This data is updated each time a domain is updated in the competitors tool.
To see inbound links as reported by Moz, check out their Open site Explorer tool. To see referral traffic in your sources report, navigate to Reports > Analytics Tools, then click Traffic Analytics.