John Owen & Thomas Boston - Distinctions: The Law of Works, The Law of Christ, the Grace of the Gospel...

Thomas Boston writes in his Notes, found in Edward Fisher's The Marrow of Modern Divinity:

No longer under Law

The law of works is the law to be done, that one may be saved; the law of faith is the law to be believed, that one may be saved; the law of Christ is the law of the Saviour, binding his saved people to all the duties of obedience, (Gal 3:12, Acts 16:31)...

The law of works, and the law of Christ, are in substance but one law, even the law of the ten commandments - the moral law - that law which was from the beginning, continuing still the same in its own nature, but vested with different forms. And since that law is perfect, and sin is any want of conformity unto, or transgression of it, whatever form it be vested with, whether as the law of works or as the law of Christ, all commands of God unto men must needs be comprehended under it...

The distinction between the law of works and the law of Christ, as above explained according to the Scriptures, and the mind of our author, is the same in effect with that of the law, as a covenant of works, and as a rule of life to believers, and ought to be admitted, (Westm. Confess. chap. 19, art. 6). For, (1.) Believers are not under, but dead to the law of works, (Rom 6:14), "For ye are not under the law, but under grace..."

"The law of Christ is an "easy yoke," and a "light burden," (Matt 11:30); but the law of works, to a sinner, is an insupportable burden, requiring works as the condition of justification and acceptance with God, as is clear from the whole of the apostle's reasoning, (Rom 3)."

The point being that the commands of the moral law are, in substance, embodied in both the law as a covenant of works and the law of Christ or third use of the law.  Both are law that command and are binding.  The distinction has to do with the "why" of obedience.  For one under the law as a covenant of works the motive to obey is fear of condemnation/death and the now false hope of meriting eternal life.  For the believer in Christ the motive to obey is gratitude born of grace with no need to fulfill the law's demands whatsoever, for Christ has finished that burdensome task:

There is therefore now no condemnation for those who are in Christ Jesus. For the law of the Spirit of life has set you free in Christ Jesus from the law of sin and death. For God has done what the law, weakened by the flesh, could not do. By sending his own Son in the likeness of sinful flesh and for sin, he condemned sin in the flesh, in order that the righteous requirement of the law might be fulfilled in us, who walk not according to the flesh but according to the Spirit. (Romans 8:1-4)

The good news is that Jesus Christ has fulfilled the righteous requirement of the law for his people.  He has born the law's penalty for sin and has also kept perfectly all the moral demands of the law.  And he has done this for all those who are his - who walk not according to the flesh (i.e. works) but according to the Spirit (i.e faith in Christ).

"The tree must first be, and then the fruit; for the apples make not the tree, but the tree makes the apples. So faith first maketh the person, which afterwards brings forth works. Therefore to do the law without faith, is to make the apples of wood and earth without the tree, which is not to make apples, but mere fantasies." (Fisher, Chapter 3:8)

John Owen writes about believers no longer under the dominion of sin (Romans 6:14), yet who find themselves still struggling against it.  Here he highlights the distinction between Christ's two words, i.e. the law and the gospel and their two different roles in the redemptive economy:

"This, then, is the present case supposed and determined by the apostle: “You that are believers are all of you conflicting with sin. You find it always restless and disquieting, sometimes strong and powerful. When it is in conjunction with any urgent temptation, you are afraid it will utterly prevail over you, to the ruin of your souls. Hence you are wearied with it, groan under it, and cry out for deliverance from it.” All these things the apostle at large insists on in this and the next chapter. “But now,” saith he, “be of good comfort; notwithstanding all these things, and all your fears upon them, sin shall not prevail, it shall not have the dominion, it shall never ruin your souls.” But what ground have we for this hope? what assurance of this success? “This you have,” saith the apostle, “ ‘Ye are not under the law, but under grace;’ or the rule of the grace of God in Christ Jesus, administered in the gospel.” But how doth this give relief? “Why, it is the ordinance, the instrument of God, which he will use unto this end — namely, the communication of such supplies of grace and spiritual strength as shall eternally defeat the dominion of sin.” 

"This is one principal difference between the law and the gospel, and was ever so esteemed in the church of God, until all communication of efficacious grace began to be called in question:  

"The law guides, directs, commands, all things that are against the interest and rule of sin. It [the law] judgeth and condemneth both the things that promote it  [rule of sin] and the persons that do them; it [the law] frightens and terrifies the consciences of those who are under its dominion. But if you shall say unto it, “What then shall we do? this tyrant, this enemy, is too hard for us. What aid and assistance against it [sin] will you [law] afford unto us? what power will you communicate unto its destruction?” Here the law is utterly silent, or says that nothing of this nature is committed unto it of God; nay, the strength it hath it gives unto sin for the condemnation of the sinner: “The strength of sin is the law.” But the gospel, or the grace of it, is the means and instrument of God for the communication of internal spiritual strength unto believers. By it do they receive supplies of the Spirit or aids of grace for the subduing of sin and the destruction of its dominion. By it they may say they can do all things, through Him that enables them.  [bracketed explanatory words and emphasis added]

[A Treatise of the Dominion of Sin and Grace by John Owen]