Depreciation and Cash Flows

I am struggling to conceptualize the relationship between depreciation and cash flows.

Depreciation is a non cash expense that is added back to Net Income in the estimation of cashflows. However, the amount of taxes saved by reporting depreciation expense is totally igonred, why is this the case?

In cash flow terms, if two companies, Company A and B report the same amount of revenue and expenses, but differ only due to the fact company A carries zero depreciation and company B carries X amount of depreciation, then surely, in cash flow terms, there should be no difference between Operating Cash Flow reported by both companies since depreciation is a non cash item, but we all know this is not the case, since company B pays lower taxes than Company A due to the amount of depreciation.

Is it possible then to conclude that even though depreciation does not directly impact on operating cash flows, it does so indirectly via the amount of cash saved from taxes?

sorry for the long post

Thanks. In this equation, why then do we add back after tax Interest but before tax depreciation? assuming depreciation is the only non cash charges?

FCFF = NI + NCC + Int(1− Tax rate)− FCInv − WCInv

Thank you for such a thorough explanation.