A corporate bond is a Treasury plus a credit spread. That decomposition is how the market thinks about it: the government leg carries interest-rate-risk, the spread leg carries default and liquidity risk, and the two can move in opposite directions on the same day.
The market splits into investment-grade and high-yield at the BBB minus / BB plus boundary, and the two behave differently. Investment grade trades mostly on rates; high yield trades mostly on equity-like default risk.
Example: a 10-year Treasury yields 4.20% and a BBB rated industrial bond yields 5.35%. The credit-spread-bonds is 115 basis points. If Treasuries rally 20 basis points and the spread widens 20, the corporate bond's yield is unchanged.
Related: credit-spread-bonds, investment-grade, high-yield, spread-duration, covenant