Although there can be an overlapping of sins with these two matters, they are stated distinctly in Exodus 20 for good reason. Here is a breakdown of the 8th commandment, ‘Thou shalt not steal’:
Stealing is to take without permission that which rightly belongs to another person. There are various reasons given in the Bible as to why stealing is wrong - a sin in God's eyes. (1) It violates the God-given law of property, first given in Genesis 2:15-17. (2) Stealing betrays a grasping spirit - see Genesis 14:11-12. (3) Stealing encourages violence - see James 4:1-3.
Sadly, circumstances may arise where some poor people feel forced to steal in order to just stay alive. This is explained in the Bible in Proverbs 30:8-9) "Keep falsehood and lies far from me, give me neither poverty nor riches, but give me only my daily bread. Otherwise I may have too much and disown you and say, 'Who is the LORD'? Or I may become poor and steal and so dishonour the name of my God." Even stealing when in dire need still dishonours God and the prayer of faith to God is that He enables us to have our daily bread, then we will not have to steal.
Also complicating matters is the fact that there is more to stealing than just lifting another person's goods. There is deceitful stealing, like insider-dealing or fiddling tax returns or expense accounts- even deliberately 'forgetting' to mention something or giving a wrong age in order to better oneself could be stealing. See Romans 13:7. There's also theft by delayed paying. Many a small business has been ruined by its debtors holding back payment beyond the agreed time limit. See Romans 13:8. There's also theft by dishonest charging, weighting scales and so on. Very often, lying and falsifying claims / declarations can be involved.
The 9th commandment is, “Thou shalt not bear false witness against thy neighbour.” The Hebrew rendered as 'false witness' (testimony) refers not just to falsifying the evidence (as can happen when breaking the 8th commandment). Although that is included, it is also to speak what is worthless, useless or unfounded. It can refer to speech that is empty of value, pregnant with dark innuendos, or a blatant lie.
Jesus also expanded on who our neighbour actually is - everyone who comes across our path - Luke 10:25-37.
Exodus 23:1-3 details how that 9th commandment is to be worked out: "Do not spread false reports. Do not help a wicked man by being a malicious witness. Do not follow the crowd in doing wrong. When you give testimony in a lawsuit, do not pervert justice by siding with the crowd, and do not show favouritism to a poor man in his lawsuit."
The Christian writer James gave the most powerful denunciation of speaking wrongly: "The tongue also is a fire, a world of evil among the parts of the body. It corrupts the whole person, sets the whole course of his life on fire, and is itself set on fire by hell (James 3:6) This includes all gossip, malicious slander, a quarrelsome spirit, hasty words, coarse joking, flattery, the silent lie and unholy lies. This latter category deals with false testimony with or about God by those who claim to speak for God. When they lie, they are false prophets. God never says the false prophets are simply mistaken, he says they are liars; “The prophets prophesy lies… my people love it this way.” “They are prophesying lies in my name” (Jeremiah 5:31 & 27:15). Well-meaning or not, a prophetic lie was punishable by death (Jer. 14:13-16; 28:16-17 Zechariah 13:3). Spiritual lying comes under a far greater condemnation from God than any other kind of lying. In the same way those who profess to teach others will be judged more strictly (James 3:1). With God there is no colour-coding for lies. White lies are like white magic, they are evil because they come from the ‘father of lies’ (John 8:44).
Once both these commandments are carefully examined, we can see the immensity of their scope. That is why it is good to keep them distinct, as does the Bible. To have a clear understanding of one, and then of the other, will help us be far more alert to the very many subtle ways in which we might slip down the slippery slope of disregarding them, or thinking they can be simplified.
Source: The Ten Commandments For Today, chapter 12, Brian H Edwards (Day One 1996)