Why are forward price and forward value not the same thing?

The forward price is the delivery price agreed to in the contract. The forward value is what the contract is worth today.

At initiation, a fairly priced forward often has value near zero because neither party should receive a free benefit. After market prices, rates, or income expectations change, the old contract can have positive value to one side and negative value to the other.

Example: If a long forward lets a fund buy an asset at 80 when comparable new contracts imply a higher delivery price, the old long forward is valuable. The delivery price is still 80; the contract value has changed.