Yes. Both NRE and NRO accounts count toward the FBAR $10,000 aggregate threshold and Form 8938 thresholds, and the interest they pay is taxable on your US return. The trap is the NRE account: India exempts its interest, which leaves no Indian tax to credit, so the US tax on it is fully payable. NRO interest is taxed in India, and the Foreign Tax Credit can offset the US tax on that portion.
Fixed deposits inside these accounts are the same story: reportable, and taxable as interest accrues or is credited.