The current yield on a bond takes into account its annual interest payment but also the price at which it can be sold.
The yield on a bond held to maturity is fairly straightforward. However, if the bond you are holding is trading at a price higher or lower than where you purchased it, the current yield would be different than the yield to maturity.
For example, if you purchased a 5% bond at a price of $100, but the current market price was $90, your current yield would be significantly lower than 5%. To calculate, simply divide annual cash inflows by market price.