Are the Old and New Testaments the same as the Old and New Covenants?

Answer 1

Yes

Additional Answer:

To be brief, the Old Testament (akin to a legal 'Will) contained a contract or divine covenant which can be compared to a divine constitution which in the Sinai or Old Covenant established a single peoples known as the ancient, national kingdom of Israel. The New Testament, in which Christ died and was resurrected, promises that the Messiah, will establish the much more inclusive KINGDOM OF GOD, that will rule over the whole earth (Isaiah 9:7; Matthew 25:14; Luke 22:29-30; Revelation 11:15). The New Covenant will become effective in the Millennial Rule and afterwards for eternity. Now we have the promise and some will find the Holy Spirit and be begotten in the God Family.

Hebrews 8:5-21New International Version (NIV)

5 They serve at a sanctuary that is a copy and shadow of what is in heaven. This is why Moses was warned when he was about to build the tabernacle: "See to it that you make everything according to the pattern shown you on the mountain."[a] 6 But in fact the ministry Jesus has received is as superior to theirs as the covenant of which he is mediator is superior to the old one, since the new covenant is established on better promises.

7 For if there had been nothing wrong with that first covenant, no place would have been sought for another. 8 But God found fault with the people and said[b]:

"The days are coming, declares the Lord,

when I will make a new covenant

with the people of Israel

and with the people of Judah.

9 It will not be like the covenant

I made with their ancestors

when I took them by the hand

to lead them out of Egypt,

because they did not remain faithful to my covenant,

and I turned away from them,

declares the Lord.

10 This is the covenant I will establish with the people of Israel

after that time, declares the Lord.

I will put my laws in their minds

and write them on their hearts.

I will be their God,

and they will be my people.

11 No longer will they teach their neighbor,

or say to one another, 'Know the Lord,'

because they will all know me,

from the least of them to the greatest.

12 For I will forgive their wickedness

and will remember their sins no more."[c]

13 By calling this covenant "new," he has made the first one obsolete; and what is obsolete and outdated will soon disappear.

In fact the Temple and Sacrificial process of the Old Covenant ended with the destruction of the Temple in Jerusalem in 70 AD. God gave the New Covenant first to the Jews and then to the Gentiles. In the Millennial rule, God's Law will be written upon all His childrens' hearts and minds. :) Read all of Hebrews for a complete overview.