A fixed deposit pays a rate fixed at the time of booking, guaranteed by the bank (subject to DICGC insurance limits), with interest taxed each year at your slab rate regardless of whether you withdraw it.
A debt mutual fund invests in bonds and money-market instruments; its value moves with interest rates and credit conditions, so returns are not guaranteed. Gains are only taxed when you redeem, and current tax treatment of debt funds has changed in recent years — check the latest rules before assuming an old comparison still holds.
FDs suit money you cannot afford to see fluctuate at all and want simple, predictable income. Debt funds suit slightly longer horizons where you can tolerate small NAV movements for potentially better post-tax outcomes and easier partial withdrawal.