Total manufacturing cost and cost of goods manufactured are used interchangeably?

No! Total Manufacturing Cost (TMC) is : Direct Materials Used (DM Beg. Bal of DM+Purchases+transport in cost-returns-End balance of DM) + Direct Labor + Overhead Applied = Total Mfg. Cost

COGM: TMC (from above) + (beg. Work-in-process - end work-in-process) =COGM