In the Greek, the same word (diathēkē) can be translated as either ‘testament’ or covenant’, so we need to look carefully at the context to determine what it should be. Hebrews 9:16 shows us that the word “covenant” can also be translated, “Testament” since the same word is used to indicate that because the death of the testator has occurred, a will is in effect.
Heb 9:16 For where a testament is, there must also of necessity be the death of the testator.
Heb 9:17 For a testament is of force after men are dead: otherwise it is of no strength at all while the testator liveth.
The word is either speaking of a covenant when two parties are involved with obligations on both, or a testament when one party is bequeathing an inheritance to another.
The KJV uses the word “testament” in 2 Corinthians 3 2Co_3:6, rather than covenant, to describe the ministry. This is because the Apostles, being stewards of the mysteries of God for His household, are distributed the riches of Christ as an inheritance for the saints (1 Cor 4:1,2; 1 Peter 4:10)
2 Cor 3:6 Who also hath made us able ministers of the new testament; not of the letter, but of the spirit: for the letter killeth, but the spirit giveth life.
Another word that is translated differently in the English according to context is Oikonomia. In the KJV, it is translated as: fellowship, communion, administration, dispensation, stewardship. It has to do with the riches in God’s household being distributed to the heirs. Consider Paul’s own description of his ministry as a steward of the riches of Christ for the gentile heirs: