Marketing Cloud Engagement - Use Mobile Lists to exclude Mobile Contacts from Messages

This is because Mobile Lists are built and reference Contacts on ContactKey, not MobileNumber or DeviceID. 
 

MobileConnect

In MobileConnect, Contacts may have more than one row attached to the Contact because there can be multiple MobileNumbers for the same Contact.

If one row's Attribute of the Contact matches the Exclusion or Suppression List criteria, that Contact will be excluded from the Send (not just the MobileNumber the Attribute matches in the Filter Criteria).

Queue MO messages will not be suppressed by Suppression Lists.

MobilePush

Only one row can be attached for the App and Device combination. If a record matches the Exclusion criteria, that Device and Contact will be excluded from any Send where the List is applied as an Exclusion. You won't have multiple rows, like you could within MobileConnect.

Suppression Lists set-up in Lists will be applied to all Sends in Mobile Connect, so no set-up is needed inside the Message itself.

Suppression lists are not supported in MobilePush, use exclusion lists instead.

See also

Using a Suppression List