I am aware that there are many different ways to measure a bonds yield including YTM and the Current Yield.
However I am not quite sure which yield is being referred to in a yield curve and other instances of a bond's yield.
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Bond returns can be broadly categorised into recurring payments and capital gains.
Recurring payments are called coupons and are usually given as a percentage of the face value of the bonds. Even if the price of the bond changes over time, the (annual) coupon rate remains constant because it is based on face value, not bond price. The bond might have provisions for changing the coupon rate under various conditions.
Expected capital gains (or losses) for bonds are calculated as the difference between (expected) sale and (actual) purchase prices. If you bought a bond for $105 and it has a face value of $100 payable at maturity, you have an expected capital loss of $5. If you sell it prior to maturity at $108, you will have an actual capital gain of $3.
Bond yields are typically quoted based on the expected coupon payments and expected capital gains to either the next call date or to maturity. They are a measure of the total gain of the bond if the bond holder doesn’t sell the bond.
You mentioned bond yield curves.
A yield curve is a line that plots the interest rates, at a set point in time, of bonds having equal credit quality but differing maturity dates. - Yield Curve, Investopedia
The coupon rates of different bonds might be different, but the yield of bonds with similar credit quality would be expected to be similar. Since the coupon rate is fixed, this means the price of the bonds change. Bonds with higher coupons tend to become more expensive while those with lower coupons tend to become cheaper. Since the yield is a measure of total return, it can give a useful comparison between bonds with different coupon rates and maturity dates, assuming continued payment of coupons and repayment of the face value, etc.
Depending upon your finance area (asset manager, loan structurer, trading, etc.) there will be different measures of yield.
However, as far as I am concerned, in fixed income trading for discussion that take place between interbank brokers, client and market makers regarding prices, and strategy or research pieces released by investment banks the same nomenclature is ubiquitous. Yield means yield-to-maturity.
Additionally other measures such as asset-swaps prices or credit spreads are calculated as the differences between two yields based on yield-to-maturity which also demonstrates its universal usage.