This thread's subject:
I would like for those who subscribe to either or both, explain/comment what those are and the difference between the two - if there is one?
Also why there appears to be such a battle going on between Covenant and New Covenant theology vs dispensationalsim?
Your title suggests there are only two covenants, but after the covenant God made with Noah and all flesh, there are a further four covenants, plus one oath:
1. The Covenant God made with Abraham, made by God unilaterally, and established by God's oath, (See Genesis 17:7-8 Hebrews 6:16-17 and Galatians 3:16-17). The promises belong to Christ and are fulfilled in and by Christ.
2. The Covenant God made with Israel through Moses (See Exodus 24:7-8).
3. The Covenant God made with king David concerning his seed, throne and royal family line (See Psalm 89:34-37 ):
I profane not My covenant, And that which is going forth from My lips I change not.
Once I have sworn by My holiness that I will not lie to David.
Once I have sworn by My holiness, I lie not to David,
His seed shall endure for ever, and his throne as the sun before me.
It shall be established forever like the moon, and like a faithful witness in the heavens. Selah. Psalm 89:34-37
4. The New Covenant, established in Christ's blood (See Jeremiah 31:31-34 and Luke 22:20).
In addition, there is the oath to Jesus in Psalm 110:4 :
The LORD has sworn, and will not repent, You are a priest forever after the order of Melchizedek.
Paul stated that the Law does not replace the Covenant God made with Abraham (see Galatians 3:17 ).
The only covenant which is replaced by the New Covenant, therefore, is the Covenant of Law made through Moses.
God's purpose has never changed and from Genesis 3:15 onward, we see God's salvation of the believing part of the Adamic race
unfolding in stages. There was never a "Plan A" until the deluge that was followed by a "Plan B". It was always Plan A - and just as Noah and his family were saved in the ark and by the ark, so with the exception of Joshua and Caleb, none of the generation which entered the wilderness, entered the promised land - only the generation born in the wilderness entered under Joshua's leadership. This is the still the status quo, today:
"And as Isaiah said before, "Unless the Lord of hosts had left us a seed, we would have been as Sodom, and would have been like Gomorrah." Romans 9:29.
Jesus came for the remnant of the house of Judah and the remnant of the Gentiles, and He has not returned yet, so His
Plan A is still unfolding before our very eyes.
Giving this fact a title ending with
.. ism just confuses the Word of God - all these
isms just add mud to the water, IMO.