Is there a difference between being saved and salvation, and the new covenant?

Incorrect. It is simply using language to give ease of communication and understanding. The same is true for translations. There is often no direct corollary from one language to another so a concept is used.

The old covenant consisted of keeping laws and periodic blood sacrifices. The new covenant is eternal in comparison because Jesus’ blood was shed once and for All people.

For the law having a shadow of good things to come, and not the very image of the things, can never with those sacrifices which they offered year by year continually make the comers thereunto perfect. For then would they not have ceased to be offered? because that the worshippers once purged should have had no more conscience of sins. But in those sacrifices there is a remembrance again made of sins every year. For it is not possible that the blood of bulls and of goats should take away sins. Wherefore when he cometh into the world, he saith, Sacrifice and offering thou wouldest not, but a body hast thou prepared me: In burnt offerings and sacrifices for sin thou hast had no pleasure. Then said I, Lo, I come (in the volume of the book it is written of me,) to do thy will, O God. Above when he said, Sacrifice and offering and burnt offerings and offering for sin thou wouldest not, neither hadst pleasure therein; which are offered by the law; Then said he, Lo, I come to do thy will, O God. He taketh away the first, that he may establish the second. By the which will we are sanctified through the offering of the body of Jesus Christ once for all. And every priest standeth daily ministering and offering oftentimes the same sacrifices, which can never take away sins: But this man, after he had offered one sacrifice for sins for ever, sat down on the right hand of God; From henceforth expecting till his enemies be made his footstool. For by one offering he hath perfected for ever them that are sanctified. Whereof the Holy Ghost also is a witness to us: for after that he had said before, This is the covenant that I will make with them after those days, saith the Lord, I will put my laws into their hearts, and in their minds will I write them; And their sins and iniquities will I remember no more. Now where remission of these is, there is no more offering for sin.

- Hebrews 10:1-18 (KJV)

I don't know that I know what the new covenant is. I believe that it is for Israel though. I am not Israel. I am a Gentile.

There was keeping laws, yes. What do you mean by periodic blood sacrifices? I know that there are specific sacrifices, but some are personal and some are regular and some are at specific times. Personal has to be with the help or by Levites though?

. . .
The new covenant is a brand new promise given by God to all who will believe in Jesus Christ and the sacrifice that He made so that we could have a permanent assurance of eternal life.

I don't believe that the Bible says this.

I have read the Bible. I do not call Matthew through Revelation the New Testament. The new covenant is for Israel. I remember Jesus brought the new covenant for Israel. I have been a Christian for about 38 years. I do not attend a local church. I do go to a synagogue. I don't know what you mean by a discipleship path. But I have been to Bible School.

I don't trust it.

John 3:16 does.

Mhmm.

With respect, somewhere along the way, you have been deceived.

A synagogue will not teach you how to maintain your relationship with God through Christ; it will teach you how to pretend to maintain your relationship with God through the Law.

As Paul wrote very clearly to the Galatians, if you want to relate to God through the Law, you must obey EVERY command... stoning adulterers, circumcising your male children (and yourself, if not done yet), and making animal sacrifices at the Temple. In case you missed the sarcasm, it is IMPOSSIBLE to follow the Law perfectly, which means you remain a sinner separated from God. As Paul wrote, "you have fallen from grace".

In the synagogue, are there ever Jewish terms used that aren't directly from the Bible?

Do you mean like Torah and the Five Books of Moses?

In 2 Corinthians 3, Paul explains the new covenant to the gentile Corinthians.

I mean are there Jewish terms that describe something but are not in the Bible?

Yes. For example, the word Torah and the words the Five Books of Moses.

Do you trust those terms?

No.

You are at least consistent. Do you trust the word Adam named things by?

I don't know what you are referring to.

Whatever language Adam used he created language for naming the animals. Whatever word he used to name birds...do you trust that word?

I don't have a problem with naming. I don't know that I can do it myself however.