Yes they are.

One recent overview Chapter Forest Ecosystem Services and Biodiversity

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should be different thing. Productivity is a kind of product provision ability, while ecological service(such as oxygen supply and carbon fixation for carbon credit for market; biodiversity maintaining and climate regulation) usually is regulation services other than visible products(e.g. timber and biomass). However, these two have closely related to each others, sometimes is positive relations.

Thanks @Wenjie, Ilan and Murray. Wenjie nice explanation - Productivity is a kind of product provision ability. My query was if ecosystem services are generated by forests then they should be part of forest productivity but is there any definition of forest productivity mentioning such. secondly any such studies done to calculate over all productivity of forests.

I agree Wenjie Wang however, what about the indirect effects of ecosystem services on productivity? For example, there is plenty of evidences about the impact of green areas over health, and of course health increase productivity. I am very interested on this issue Manmohan J. Dobriyal and I think it has not been enough considered in literature.

Yes，I aggree with that this should be considered in future studies. Usually, there is a tradeoff between different ecological services, and sometimes with the productivity of biomass.

Yes

Productivity is the basic foundation. It provides all ecosystem services. Apart from Provisioning and regulating services, the supporting of life cycles of different flora and fauna is regulated by the forest productivity.

Without plants ( primary productive) cannot form an ecosystem. So any services depends the plants and I agree Wang statement

Yes, they are. There is research in Peru to prove it. You could check this link: https://repositorio.up.edu.pe/bitstream/handle/11354/2217/DT97.pdf?sequence=1

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This article would be useful.

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