What is the difference between, Cannot sin and did not sin? Cannot sin and without sin?

as you put forth the bible says Jesus was tempted which means He could sin, but He did not

'Can not' implies incapacity

'did not' implies capability. 

Jesus was certainly capable of sinning, that is why when he was in the wilderness fasting for forty days, Satan came to tempt him. 

In the verse you ask about, Paul was saying that Jesus was without sin because he did not sin.  

(1 Peter 2:22)" He committed no sin, nor was deception found in his mouth".

Like all Jehovah Gods creations Jesus also had the choice of free will. And unlike the spirit creature who became known as Satan chose to sin, Jesus died free of sin and faithful and was resurrected to immortal life in heaven to rule as King of God's Kingdom.

Jesus was the only person to have ever been born without the sinful nature (since Adam*), i.e. as the alpha and omega, the only One of His kind, the promised Christ, the Messiah. I suppose you could call this the ultimate test of the ultimate power and sovereignty of the Holy Spirit, by which Jesus was conceived.

So it was not that Jesus was unable to sin and you are right that He would not have been tested otherwise, but that He was simply strong enough to resist every and any temptation and that, as you may well know, is one of the promises which were made …..  that in Him, His followers are able to overcome the world, no matter what it throws at them, even up to the point of death, I believe.

* Note that Adam was the first to have the spirit of man breathed into him and at that point he was pure and perfect but fell from grace through temptation. He was not, however, conceived of the Holy Spirit otherwise he would have known or been strong enough not to yield to that temptation and would have remained sinless and probably childless so we might not actually exist if that had been the case …. ?

What this seems to indicate or prove is that without that spiritual assistance man is unable to resist yielding to temptation and so if left unaided a spirit will begin the downward spiral or slippery slope of the law of sin and death and our spirits will become dead ones.

Jesus clearly demonstrated that He was God, by constantly doing things only God could do. God cannot sin, since sin by definition is something opposed to the will of God.

Please answer the actual question.

Jesus was continually tested, Mt. 4:1-11. The context of Hebrews reveals that Jesus is the perfect high priest.

One who has born from holy spirit, evils do not able to pull him on their path. So he does not commit sins. Disciples of saints are at different levels. 

Path of saints (inner).

I understand your confusion, but you are talking about two different aspects of God.  

God the Father cannot sin.  Jesus the Son was fully human and fully God, and had all the human capabilities to sin, but chose not to when tested.

JESUS WAS tempted by the devil but never sinned..