MOZ and Majestic metrics are refreshed weekly on the platform.
The metrics on their own websites are refreshed multiple times a day and will, therefore, be more accurate in most cases.
The metrics on the platform are there to provide a guide to the site's metrics and the differences should be minimal.
For Majestic, the platform checks the metrics for the root domain, without Http:// and without www, per Majestic’s recommendation.
For MOZ the metrics for all URLs are the same.