Yield Curve = Forward Curve?

No, the yield curve of a bond and the forward curve of a bond are not interchangeable terms. While they are related, they represent different concepts.

Yield Curve:

Represents the relationship between the yield to maturity and the time to maturity of bonds with the same credit quality.
It’s a snapshot of the market’s expectations of future interest rates at a specific point in time.

Forward Curve:
Implies expected future interest rates based on the current yield curve.
It’s derived from the yield curve using arbitrage-free pricing models.
Represents the market’s expectations of future short-term interest rates.

P/s: super mario 64