It is expected that at times the costs in the Anomaly report will different from what's shown in the Cost History report.
You may see a cost difference because the Anomaly report shows costs for all services and excludes monthly cost for reservations (e.g. No Upfront RIs, All Upfront RIs, etc). CloudHealth exclude's reservation costs from Anomalies, because this monthly expense is a commitment you've already made in advance and is not an unexpected spike in costs. However, the Cost History report shows costs for all services and includes monthly costs for reservations.