I was able to find a good answer that was previously posted here: https://community.shopify.com/c/Shopify-APIs-SDKs/Get-order-s-sales-channel-name/m-p/324788/highligh...
In some cases, the source_name will be set to a reserved value such as web or pos to denote that the order originated from Shopify Online Store or Shopify POS.
For any third-party sales channels, the value is set to the app id of the sales channel. If you know the app id of the Amazon channel (by inspecting a known order), for example, you could build a mapping service on your end.
580111 is also the online store or "web" - depending on how the order is created, it will sometimes be saved as the ID.