Outbound-api and outbound-dial are values in the "Direction" column of a call report.
Outbound-api is an outgoing call made using the API (most likely through the call connect API). Example: a Click to Call which is made through API which is integrated with any of the CRM using the connect API.
Outbound-dial is an outbound call made from either the dashboard (through the call button or campaign etc.) or the smartphone app.