If you're looking at the SMS Messages table for data mapping, you'll notice there is Owner Id (mercury__Owner_Id__c) and Owner (OwnerId).
These have similar names, and are basically the same thing when sending outbound messages – but they'll have different meanings when the customer replies.
For replies, “mercury__Owner_Id__c” records the original Salesforce user that send out sms. For Inbound SMS the Owner (OwnerId) refers to the system user, like “Automated Process”