Bonds and bond funds are both considered safe investments when held to maturity. Bond funds even out the risk across all the different types of bonds that they own, making them objectively safer than individual bonds which can go into default if one company goes under.
The interest rate on a bond fund is dependent upon the interest rates that have been set by its underlying bonds.
Bond funds are considered a lower risk investment than individual bonds because they usually invest in a portfolio of different bonds. This diversifies the risk.
Bond funds also give savers access to specific types of bonds that they may not be able to afford on their own (foreign, junk, etc).
On the other hand, individual bonds are often able to offer higher yields than bond funds because they lack diversification. Bond funds also typically charge higher fees than individual bonds.
Bond funds are generally only able to be purchased through investment intermediaries, such as a bank or brokerage firm. Individual bonds can be purchased directly from the government (treasury bond) or corporation (corporate bond bond).