Hi @sarah-flint
The source_name of an order will change depending on how the order was completed. If the draft order is completed by an app, completed by the customer via checkout or completed directly in the admin the source_name will vary.
If the draft order was completed by the customer following the Complete Purchase option from the email invoice paying via the online checkout the source_name will show as web.
If you complete the Draft Order via an app like the one used to create the draft order, the source_name will show as the app ID.
If you complete the Draft Order from the Draft Order section of the admin the source_name will show as shopify_draft_order.
I hope that helps in understanding the behaviour around the source_name field.