Some small finance banks have equal or better interest rates and are insured. Again that's not the point. My point is why call it "Fixed Deposit"? I see it as a clear breach of public trust. They could have called it Super Deposit/Vijay Malya Punarvikas Fund or anything else but FD.
Edit: Fixed Typos
You are wrong in assuming that it is totally correct to call TERM DEPOSITS as Fixed Deposits. They are not Fixed in the true sense. A Bank FD (as you call a Term Deposit) is exactly not a fixed one - it can be withdrawn - prematurely - by losing some agreed interest.
However, the deposits with these NBFCs are TRULY FIXED DEPOSITS. No premature withdrawals or no loans/overdraft given against them.
DICGC coverage is mandatory for bank deposits - but not so for NBFCs - generally speaking.
Of late, NBFCs are also offering some hybrid models - loans against FDs, Credit/Debit cards against FDs - which work on ATMs,.....
Having worked extensively in Rural, Semi-urban, Urban, Metro n Specialized branches - for close to 40 yrs - be rest assured that the bank customers are well informed - more so - the TDR/STDR customers.
And, despite better rates offered by NBFCs, they find it difficult to get customers for their FDs. And, banks have reached almost every nook n corner - unlike NBFCs.
Well informed n risk taking investors (like me) also invest in NBFC FDs - like any other alternatives like NCDs, PCDs, Shares, TF Bonds, G-Secs, Gold Bonds....
As you are aware none of these have any insurance cover - some have Govt guarantees.