The traffic referrals report only records clicks with referral URLs set. Clicks without referral URLs are not shown in the traffic referrals report. So if clicks in the stats report don’t match clicks in the traffic referrals report, then not all of your partner traffic has referral URLs.
It’s standard that about 80% of traffic doesn’t have a referral URL. This can be much higher if your users have additional security settings in place, or if the traffic is from an ad network or partner that hides their traffic URLs.