All perfect praise be to Allaah, The Lord of the worlds. I testify that there is none worthy of worship except Allaah and that Muhammad is His slave and Messenger.
What you have concluded and attributed to Ibn Abbaas that the verse in question is specific to someone who repented from Shirk (polytheism) is incorrect. Ibn Abbaas stated about the reason of the revelation of the verse that it was revealed in connection with some people from the polytheists who committed abundant killing and Zina (fornication or adultery) and asked the Prophet about the expiation for this, then Allaah sent down this verse. Nonetheless, the fact that this was the reason for the revelation of the verse, according to Ibn Abbaas and others, does not necessarily mean that it does not include people other than them.
Ibn Hajar said in Al-Fat-h, “After the revelation of the verse {Say: O My servants who have transgressed against themselves [by sinning]…} [Quran 39:53], in the narration by At-Tabaraani: 'So the people asked the Prophet O Prophet, we have done what Wahshi has done (i.e. we killed people), and the Prophet replied, It is for all the Muslims.”
Also, Ahmad and At-Tabaraani reported in Al-Awsat from the hadeeth by Thawbaan, who said:
“I heard the Prophet say, 'This verse is better for me than the whole world and whatever it contains: {Say: O My servants who have transgressed against themselves [by sinning]…};' then a man asked, 'What about somebody who committed Shirk [and then repented]?' The Prophet kept silent for a while and then responded to him, 'Even if he committed Shirk,' and he repeated this three times. The scholars used the general meaning of this verse as evidence that all sins can be forgiven, regardless of whether they are major or minor sins and whether or not they are related to the rights of people. The well-known opinion of Ahlus-Sunnah is that all sins are forgiven with repentance and that these sins are forgiven for whomever Allaah wishes to forgive them, even if he died without repenting. But as for the rights of the people, if the one who transgressed against them repented, then repentance will benefit him as regards refraining from transgressing against the rights of others, but he must give the people back their rights or seek their forgiveness. Yes, it is from the vastness of the Mercy of Allaah that He may please the owner of the right so that he relinquishes his right and Allaah then does not punish the transgressor, and this is indicated by the general meaning of the saying of Allaah (which means): {Indeed, Allaah does not forgive association with Him, but He forgives what is less than that for whom He wills.} [Quran 4:48]”
If someone who committed Shirk is forgiven when he repents, then someone else whose sin is less than this is to be forgiven with greater reason if he repents. Ibn Abbaas and other scholars did not say that the sins are not forgiven if someone has repented from them so that this would cause confusion to you regarding what he mentioned about the revelation of the verse and you attributed this saying to him.
What should be taken into account, as has been determined by the scholars, is the general meaning of the words, and not the occasions because of which they were revealed (i.e. it is the general linguistic indications of the text that establish a normative understanding, not its context).
Also, regarding the confusion that you mentioned about other statements of Ibn Abbaas, please mention those statements so that we can give you an appropriate answer. It might be that the confusion is in your understanding, as is the case in regard to the above issue.
Allaah knows best.