A more thorough explanation:

Yield spread refers to the difference in yield between different securities issues. It is the difference between the yield on a higher-risk investment and a lower-risk investment.

For example, if a 10-year Treasury bond has a yield of 2% and a corporate bond with the same maturity has a yield of 4%, the yield spread between the two is 2%. This means that investors are demanding a higher return for taking on the additional risk of investing in the corporate bond.

Yield to maturity is the rate of return an investor can expect to earn if they hold a bond until it matures. It takes into account the bond's current market price, its face value, the coupon rate, and the time remaining until maturity.

Suppose an investor purchases a bond with a face value of $1,000, a coupon rate of 5%, and 5 years remaining until maturity. If the bond is currently trading at $950, the yield to maturity would be higher than 5% because the investor is buying the bond at a discount. If the bond were trading at $1,050, the yield to maturity would be lower than 5% because the investor is buying the bond at a premium.