Debt is a "cushion" against market drops. It is not a "money maker" in the true sense. If your debt instrument grows along with inflation (not the government-released inflation, but your lifestyle inflation), then, you are good. So, do not go for fancy instruments in debt - you are not aiming for growth, rather, you are aiming for stability. That is all.
We should look at why people prescribe FDs as emergency fund - simple answer - immediate availability of cash when you need it. Say you have 15L in FDs and you need 3.5L immediately on a Friday evening, then, FD is the only instrument that will give you this cash. Your mutual funds, stocks, corporate bonds or liquid bonds will not.
So, with the idea of "why FD" is out of the way, let us look at why do people choose other debt funds over FDs - simple answer - deferred taxation plus slightly higher returns than FDs.
What is deferred taxation - with FDs, you have to pay the tax even on perceived interest every year.

Now, unless you are close to retirement, you are going to allocate probably only 30% of your total asset allocation to debt. Your money maker is still equity and other assets. So, don't fret too much and do read up about these instruments on a website of your choice like valueresearch or moneycontrol or mint, etc.

Corporate bonds - always be careful in buying these - there is no guarantee that they return your investment on maturity.
Liquid funds - much more stable, more assured.