Does the mention of Qur’anic ayat being subjected to abrogation – nasikh – or being abrogated – mansukh – mean it is true that ayat have been omitted from the Qur’an?
Is the Qur’an used by Shi’ites any different from the Qur’an used by Sunnis?

Not a single ayah of the Qur’an has been lost. It is totally incorrect to think or to claim that Shi’ah and Sunni Muslims have different Qur’ans.
All Muslims hold the view that there have been no alterations made to the Qur’an and that the Qur’anic text is Allah’s complete revelation to the Holy Prophet (PBUH). A large number of prominent Shi’ah scholars, including the leading traditionalist Ibn Babawayh acknowledged this. At the beginning of his exegesis of the Qur’an ‘al-Tibyan’, Shaykh al-Tusi expressed the same view and stated that the most comprehensive evidence had led his teacher, al-Sharif al-Mortada, to accept it. Shi’ah scholars do indeed believe that no alteration has been made to the Qur’an.
As far as nasikh and mansukh are concerned, the most comprehensive and scholarly research into this subject of ayat abrogation, is to be found in the late Ayatollah al-Khoei’s, The Prolegomena to the Qur’an – al-Bayan. In brief, many Sunni scholars deliberate over the recitation of an ayah being abrogated without its ruling in Islamic law being abrogated.
The ayah about stoning is cited as an example of this type of abrogation. Those who maintain this, claim that that ayah was once part of the Qur’an, but that when its recitation was abrogated, its ruling in Islamic law remained effective. This is claimed in Sahih Bukhari, Vol. 8, p. 26 and Sahih Muslim, Vol. 5, p. 116, to have been related from ibn Abbas. They say that Umar proclaimed from the dais – minbar – ‘Truly, Allah sent Muhammad (PBUH) with the truth, and revealed to him the Book. Among those ayat Allah revealed is the ayah about stoning, which we read, understood and acted on. The Messenger of Allah (PBUH) accordingly stoned fornicators, and we continue so to do. However, I am afraid that with the lapse of time, someone might say, ‘By Allah, we did not find the ayah about stoning in Allah’s Book’ and thus, be misguided into forsaking this obligation revealed by Allah. Indeed, stoning is certainly prescribed in Allah’s Book for those who commit adultery …
Our comment regarding such a view is that its documentation is based on a single narration,
and as such, cannot be considered if one’s objective is to arrive at an authoritative ruling.