One-liner
Market value is what a bond is worth if you sell it today, and it moves up and down with the market's mood. The curve is the return you when you bought, building steadily toward maturity, where the price finally lands no matter the bumps along the way, as long as the issuer pays.
- Curve: contracted return
- Market price (secondary)
Why it matters
Most people buy fixed income thinking the value is known and the growth is fixed and predictable. But the market prices it day to day, so it swings. It swings enough that some fixed income is riskier than stocks.
Analogy
You pre-order a PlayStation 5 for delivery on a set date; Sony hands it to you that day no matter what (the curve). While you wait, the price of an incoming PS5 like yours moves: demand spikes and supply gets tight, so what someone would pay for your order goes up; demand cools and the market would offer you less. None of that touches you unless you sell. Hold to delivery and you get your PS5, full stop. Flip it early and you take whatever the market pays that day, above or below what you put in.
The catch
Fixed income is not fixed while you hold it. Between purchase and maturity it can swing a lot, and the longer the the more.