Bond interest rate is another commonly used name for a bond's coupon rate: the fixed annual rate stated on the bond at issuance, which determines the dollar amount of cash interest the issuer pays bondholders each period, calculated as that rate multiplied by the bond's face value.
Why several names describe the same figure
Depending on the context, this same stated rate is called the bond interest rate, the coupon rate, the nominal rate, or the face interest rate, and all four terms refer to the identical fixed percentage printed on the bond — none of them changes once the bond is issued, regardless of how market interest rates move afterward. Which label a particular textbook, lender, or offering document uses is simply a matter of convention rather than a difference in meaning.
Where to go for the full explanation
See Bond Coupon Rate for a complete explanation of how this rate is set relative to prevailing market interest rates at issuance, why it determines whether a bond sells at a discount or premium to face value, and how it differs from a bond's yield to maturity, which captures the bond's true total return rather than just its stated interest rate.