Old Testament - The system of law instituted at the creation (and maybe before) by our Eloah, whose name is Yahuwah to the all the people of the world. Also called the Ten Words (Commandments).
The Law of Mosheh - given by Yahuwah to Mosheh at Mount Choreb. It was intended to separate the Yisra'eliym from the rest of mankind. It became of force at Shemot (Exodus) 24:8.
The Ibriy (Hebrew) scripture is the collection of books from Genesis through Mal'akiy (Malachi). The first five books are also commonly called the books of Mosheh, Pentateuch, and the Torah. Major divisions within the Ibriy scriptures are the law, prophets, and writings. Followers of "Judaism" call their scripture the TANAKH, meaning the Torah (law), Nawbiym (the prophets), and Kethuwiym (the writings).
There are many other divisions that can be made also, such as from the creation to the flood, the flood till Abraham, etc.
New Testament - This system of the law of our Eloah, also called the Law of Grace, the Perfect Law of Liberty, etc., supplants the first law and Law of Mosheh, which had served its purpose as a schoolmaster (Galates [Galatians] 3:24) to bring us to the Anointed. It became of force at the death of the Testator, Yahushua, who is the Anointed. MattiythYahuw (Matthew) 27:50, Markos (Mark) 15:37, Loukas (Luke) 23:46, Yahuchanan (John) 19:30. Also see Ibriym (Hebrews) 9:ALL.
Some more divisions
The Greek scripture is the collection of books from MattiythYahuw (Matthew) through Revelation (the apocalypse). The first four books are commonly called the Gospels, or good news, because they tell the story of Yahushua's birth, life, death, and resurrection. Major divisions within the Greek scriptures are the Gospels, the acts of the Delegates, the letters (epistles), and the revelation (apocalypse).
The Gospels tell who Yahushua is, why He was here, and what He did while He was here. Also, they tell the reason why people must believe that He is the Son of our Eloah and give the proof of that belief. (Why you need salvation.)
The acts of the Delegates tells the story of the ascension of Yahushua to our Father, the Grand Opening and formation of the Assembly, and what the individual must do to become a part of that Assembly. What was done then is what we must be doing today. (How to attain salvation.)
The letters are all to believers who have truly repented and been immersed according to the will of our Eloah and tells them how to grow as His children and to stay in that condition. (How to keep salvation.)
The apocalypse is to those same people telling them in detail what is going to occur in the last days. (What is going to happen to those who do not believe and obey.)
The words covenant and testament as found in the Ibriy and Greek scriptures are translated from the same Ibriy and Greek words, respectively. They mean the same thing in both languages (a contract, or agreement between two or more parties) and are interchangeable with one another.
Prior to the Law of Mosheh being given Yahuwah made several covenants or testaments with various people such as Adam, Noach (Noah), Abraham, Yitschaq (Isaac), Ya'aqob (Jacob), etc. Some of these covenants or testaments were much older than the Law of Mosheh and could reasonably be called "old testaments." In the scripture whenever the phrase "old testament" is used it is always referring to the Ten Words. The common belief that the Old Covenant or Testament is all of the Ibriy scripture is therefore in error and can do nothing but lead to more error in the person who is trying to learn of the word of Yahuwah.
The Ten Words and the Law of Mosheh were in effect until Yahushua died as He showed throughout the Gospels by telling people such things as to "show themselves to the temple official (kohen) as says the Law of Mosheh." As the Lawgiver Himself, He also obeyed the Law of Mosheh. (The laws that He was always being accused of violating were not those of the Law of Mosheh, all of which at that time were valid, but those of the "oral Torah" or the laws of man's tradition which were not valid.) Therefore all of the Greek scripture cannot be the New Covenant or New Testament. This error also leads to confusion and lack of understanding of the word of Yahuwah.
The easiest way to understand this is that all of the law of Yahuwah, both the old and the new covenants plus all other covenants that Yahuwah made with various people, are contained in scripture, but the scripture is not the covenants. The scripture then is a collection of the morally clean books and letters written by men inspired of Yahuwah to write them. In these books and letters will be found His law.