Difference between Value-Added TFP and Gross-Output TFP?
Your assumption is correct.  Value added is Gross Output-intermediate consumption(inputs). 

value-added approach is a simple measure that ignores the difficulties of dealing with inter-industry and intra-industry flows of goods and services. Intermediate inputs are simply excluded here. 

The value-added approach provides a simple link of industry-level MFP
and sectoral or aggregate MFP growth.

For gross output-based estimates of MFP growth they acknowledge and allow for intermediate inputs as a source of industry growth. In this method they provide a more complete picture of the production process.

If you need more information this manual can help: https://www.pc.gov.au/research/supporting/comparison-gross-output-value-added-methods/cgovam.pdf