The words covenant and testament are generally synonymous in the text of the Bible. That can lead to a misunderstanding because the word testament has also been used to name the two major sections that men have designated in the Bible: Old Testament and New Testament.
The confusion arises because each section contains scriptures that relate to other covenants besides the one for which it is named. The Old Testament refers to other covenants in addition to the one that God specifically calls the Old Covenant, the covenant that he made with Israel at Mt. Sinai. The New Testament contains the scriptures pertaining to the New Covenant, which were written to believers in Jesus Christ, but it also includes the four gospels, which actually occurred during the Old Covenant. The New Covenant did not begin until Jesus shed his blood and died on the cross.
For the sake of clarity in this book, Old Testament and New Testament will be used in reference to the two sections of the Bible. Old Covenant and New Covenant will refer to those two covenants specifically. The Bible also refers to the Old Covenant as the law of Moses or just the law. In this book the word law is capitalized when referring to the Old Covenant—the Law. When the word law is not capitalized it is referring to any other law or law in general as a principle.
This book uses the words man and son from a spiritual perspective. The term man is used in reference to mankind, anyone of the human race, male and female, regardless of age. All references to sons of God in this book include born-again women just as much as born-again men. In Christ there is neither male nor female. (Gal. 3:28) Women in Christ are sons of God, equally as men.