All three covenants are mentioned in the book of Hebrews (Heb. 8-9; 13:20). In a nutshell the difference is that the "old" and "new" covenants are divine in origin but human in administration and the human administration is declarative in nature but the human administrative aspect actually saves no one. The human administrative aspect is clearly stated in Hebrews 9:1. Then verily the first covenant had also ordinances of divine service, and a worldly sanctuary. - Heb. 9:1 Whereas, the "everlasting" covenant is divine in origin WITHOUT human administration but is directly administered by God to His elect in all ages from Genesis to Revelation and is always effectual to salvation. Actual individual salvation has always been by direct administration of the Triune God in all ages. No salvation has occurred by any human administration or time restricted covenants. A. The "Old" covenant There can be no argument that the "old" is divine in origin but human in administration. There are ordinances, house of worship, a qualified human ministry (Heb. 9:1). Neither can there be any argument that its design was never to actually justify anyone, or save anyone but only designed to instruct them in the nature of sin (Rom. 3:20; Gal. 3:21-22) and declare God's eternal purpose of salvation in TYPES and SHADOWS. Actual salvation from Genesis to Christ was through the preaching of the gospel of the anticipated Christ (Acts 10:43; Gal. 3:8; Heb. 4:2). This is primarily a Jewish covenant although there is a limited gentile inclusion. B. The "New" covenant. - Heb. 9:1 Then verily the first covenant had also ordinances of divine service, and a worldly sanctuary. - Heb. 9:1 It is called "new" in reference to the "old" as the former preceded it in time. However, it too had a point in time for its existence and it too has a human administration, ordinances, a public house of worship, and a qualified ministry. The difference between the "old" and "new" is that of anticipation versus fulfillment of the promised Christ. However, the human administration of the "new" does not save anyone any more than the "old" but instead is declarative of the fulfilled gospel of Christ wherein the power of God unto salvation has existed and has been applied since Genesis before either the "old" or "new" existed. This is not merely a Jewish covenant but the work of the Holy Spirit exceeds the boundaries of Judaism and primarily is Gentile in its redemptive extent. Hence, the Holy Spirit's work of salvation under this covenant is more extensive "all flesh" instead of merely Jewish. C. The Everlasting Covenant Now the God of peace, that brought again from the dead our Lord Jesus, that great shepherd of the sheep, through the blood of the everlasting covenant, - Heb. 13:20 This covenant is not time restricted. It is the "eternal council" of God that has existed as long as God has existed. There is no point in time when it came into existence. There is no human administration of this covenant but this covenant is between the three Persons of the Godhead and they each administer aspects of this covenant directly to the elect in all ages. The "old" covenant declared it in types and anticipated the cross in time. The "new" Covenant declares it directly and clearly based upon the fulfillment of the cross but still anticipates its completeness yet in the future.The "new" covenant is not the fulfillment of the everlasting covenant - that still awaits beyond this present time and earth. Application of the "everlasting covenant" is not time restricted but its application is based upon the eternal purpose of God before the world began and God views events in time as an everlasting present "I AM" that treats things not yet accomplished in time as already completed (Rom. 4:17) and therefore God acts as though they are completed because from his point of view there is no past, present or future but just one eternal present based entirely upon his eternal purpose. When the events occur in time they simply justify God's application in time prior to that fulfilled event (Rom. 3:24-25). God's application is based on the promise according to His eternal purpose (Rom. 8:28-37) rather than the actual time of the fulfillment of that promise. God sees "the blood" slain from the "foundation of the world" and acts upon it the very same way because what he has purposed before the world does come to pass as predicted. Hence, God's word is sufficient to apply his redemptive purpose any time within time.