The Idea in Brief
Liars tell lies, but the false witness also includes those who may tell the truth, but are malicious people who therefore "lie" against the truth. When liars lie, they are false witnesses, but not all false witnesses tell lies (notwithstanding that they still "lie" against the truth).
The Book of James provides the framework for understanding the arrogant, lying, murdering, wicked evil heart in addition to the "malicious" false witness found in the Book of Deuteronomy.
The Book of James appears to provide the parallel explanation and clarification of these verses in Proverbs.
Proverbs 6:16-17 (NASB)
16 There are six things which the Lord hates,
Yes, seven which are an abomination to Him:
17 Haughty eyes, a lying tongue,
And hands that shed innocent blood,
The "haughty eyes (proud) look, lying tongue, and hands that shed innocent blood" speak of the so-called brother who kills others with his words.
James 3:14 (NASB)
14 But if you have bitter jealousy and selfish ambition in your heart, do not be arrogant and so lie against the truth.
This verse (above) is the capstone of the previous verses of James 3:1-12, which speak of the power and destructiveness of the human tongue, which is equated with homocide in James 2:11. In other words, the "haughty eyes (proud) look, lying tongue, and hands that shed innocent blood" speak of the so-called brother who kills others with his words.
Proverbs 6:18 (NASB)
18 A heart that devises wicked plans,
Feet that run rapidly to evil,
The Book of James also addresses the motives of the heart, which finds expression in evil.
James 3:8 (NASB)
8 But no one can tame the tongue; it is a restless evil and full of deadly poison.
James 3:16 (NASB)
16 For where jealousy and selfish ambition exist, there is disorder and every evil thing
James 4:16 (NASB)
16 But as it is, you boast in your arrogance; all such boasting is evil.
Finally, James discriminates the difference between the lying tongue and the false witness, who spreads discord among the brethren.
Proverbs 6:19 (NASB)
19A false witness who utters lies,
And one who spreads strife among brothers.
But first we must note one point. The term "who spreads" highlighted, above, in Hebrew is וּמְשַׁלֵּחַ, and occurs in the Piel Stem (intensive) Present Active Participle (Masculine Singular). That is, the triliteral stem שָׁלַח means to send, but in the intensive stem (Piel), the word means to disseminate, to send or spread out, or to shoot off (for example, arrows as in 1 Sam 20:20).
So in James we find the following passage in this regard ("shooting off the mouth") in the context of the false witness among brethren.
James 4:11 (NASB)
11 Do not speak against one another, brethren. He who speaks against a brother or judges his brother, speaks against the law and judges the law; but if you judge the law, you are not a doer of the law but a judge of it.
James 5:9 (NASB)
9 Do not complain, brethren, against one another, so that you yourselves may not be judged; behold, the Judge is standing right at the door.
The "false witness" is not just about lying (Prov 6:17), but has to do when there is only one person who is accuses one other person before the presence of others (without the involvement of any second witness), which thus constitutes the "bearing false witness."
Deuteronomy 19:15-17 (NASB)
15 A single witness shall not rise up against a man on account of any iniquity or any sin which he has committed; on the evidence of two or three witnesses a matter shall be confirmed. 16 If a malicious witness rises up against a man to accuse him of wrongdoing, 17 then both the men who have the dispute shall stand before the Lord, before the priests and the judges who will be in office in those days.
The context in the verses, above, is about one person accusing one other person. Even though the accusations may be true, the accusing in the absence of the second witness constitutes false witnessing against ones neighbor. That is, James is condemning the accusations of the "one-on-ones." The Law of Moses demanded that at least two witnesses accuse the third party, because in such cases the problem would not be confined to one person against another, but against the collective interests of the wider community.
The lying tongue tells lies, but the false witness does worse: he can tell the truth, but in the absence of another witness (to testify against the third party), that person lies against the truth. That person is indicative of maliciousness, which spreads strife (like shooting arrows) among the brethren. In this sense, that person is the false witness, who promulgates discord (like shooting arrows) among brethren.