The coupon is fixed in dollars; the yield is that income measured against what you actually pay. Yield to maturity goes further and includes the pull to par, the gain or loss from holding a bond bought above or below its face value until it repays.
When people say yields rose, they mean bond prices fell. The two are two descriptions of one movement, and headlines use them interchangeably.
The spread between a corporate bond’s yield and the matching Treasury is the credit spread, the extra compensation demanded for default risk. Widening high-yield spreads are among the earliest and most reliable warnings that financial conditions are tightening.