The first usually signifies a two-party agreement under seal, where benefits are conferred on one party in return for certain observances by the other. A ‘testament’ is a unilateral disposition of property by will, as in the phrase, ‘last will and testament’. It takes effect on the death of the testator. In the New Testament the choice between the two words seems to depend on the aspect to be emphasised. In the Old Testament the Mosaic covenant was sealed with the blood of sacrificial animals.
To use the word ‘covenant’ in the present context would seem to emphasise the continuity of the need for a sacrificial shedding of blood, in this case, Christ’s, as the seal necessary for the validity of the covenant. The choice of the word ‘testament’ would tend to look ahead not only to Jesus’s death but also to what follows from it. (See Hebrews 9:15-22.) This is perhaps why the same Greek words are invariably translated ‘the New Testament’ when applied to the second ‘half’ of the Bible.