Do we gain thawab for the sins we abandon?

If we do something inherently right (ie. be truthful in a scenario where it may be difficult), is it recorded as a good deed or simply "not a sin"?

When we do something right, like telling the truth, we do not just abandon a sin but gain thawab as well

A person’s being righteous is a sign of his “faith” His abandoning lying despite being in a difficult situation, certainly causes him to gain thawab. Since he obeys the Quranic order “and shun lying speech.” (Surat-u Hajj; 30),he gains the reward of obeying his Lord (swt). Thus it is narrated as a good deed. As mentioned above, even just abandoning the sin or giving up committing a sin is also recorded as thawab.

Narrated Ibn-I Masud;

"Truthfulness leads to righteousness, and righteousness leads to Paradise. And a man keeps on telling the truth until he becomes a truthful person. Falsehood leads to Al-Fajur (i.e. wickedness, evil-doing), and Al-Fajur (wickedness) leads to the (Hell) Fire, and a man may keep on telling lies till he is written before Allah, a liar." (Sahih Bukhari, Muslim, Muwatta, Abu Dawuud; Tirmidhi)

Malik related to me that he heard that Abdullah ibn Masud used to say, "You must tell the truth. Truthfulness leads to right action. Right action leads to the Garden. Beware of lying. Lying leads to corruption, and corruption leads to the Fire. Don't you see that it is said, 'He speaks the truth and acts rightly,' and, 'He lies and is corrupt.' " (Muwatta, Book 56)

Even abandoning the sins causes us gain reward and is recorded as thawab

Badiuzzaman Said Nursi, one of the scholars of this century, stated in his tafsir that in this era which is the end of the world, one who performs the fard (obligatory) and abandons the major deeds reach safety. Pointing out to the importance of righteous deeds, he stated that a small amount of righteous deeds equals to great amounts under these circumstances. A little deed that was performed on the condition of abandoning hundreds of attacking sins causes rewards of hundreds of wajibs.

Regarding these words, we understand that in such a dreadful time, if we abandon the sins with taqwa, we will gain as much rewards as performing hundreds of wajib. And these rewards will appear on the right scale and compensate many sins on the Day of Judgment inshallah. This is the special bounty of Allah (swt) for the people of this dreadful century.

Man will get the reward and the penalty for each of his deeds regarding the principle “The deeds are considered by the intentions.” If a deed is not performed to gain the consent of Allah (swt), it does not cause thawab and it can be means of sin, as well. Just as “the life of deeds is intention”, certainly a deed performed with a sincere intention or abandoning a sin to cause the consent of Allah (swt) is superior to a great number of deeds. Besides, they will be a means of increasing the good deeds in the hereafter inshallah.

Abandoning the sins is the most superior worship

Hadrat Aisha stated that:

“You overlook the most superior worship. It is vera, abandoning haram.”
Abdullah ibn-I Omar stated that:
“Even if you perform salah until you bend like a bow and even if you fast until you slim like a wire, they will not be accepted from you until you have ‘vera’ that avoids you from haram.” (Ihya-yi Ulum-id Din)