You mean this only for cash US dollar - i.e. physical bills? Not USD in bank accounts?
1. Spending dollars on US soil from an US bank account won't incur extra fees (at least visible to the person - I know about interchange fees, but they are borne by the merchant), while using card issued by a foreign bank can incur fees for cross-border transactions (at the level of 2-3% usually).
2. Sanctions and KYC concerns also make different dollars have different value. Money in US bank account of an US company employee can be used at face value - money in some less-favored country bank, not so much.