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.
First of all, we should say that it is known that the place of intention is the heart and not the tongue, so the utterance is not the intention; rather, it [utterance] is speaking out loud the intention which is in the heart. Indeed, there is no contradiction between the two Fataawa of Shaykh Ibn Baaz to which you referred because the Fatwa in which he stated that it is an innovation to utter the intention, was a reply to a question about the ruling of uttering the intention in the prayer and not in Hajj and ‘Umrah as per the question of that Fatwa in his "Majmoo’ Al-Fataawa".
We will hereby mention the whole Fatwa from "Majmoo’ Al-Fataawa Ash-Shaykh Ibn Baaz" exactly as it is in volume no. 10 page 423:
Question: A questioner from Egypt asks: What is the ruling of uttering the intention loudly in the prayer?
Answer: “Uttering the intention is an innovation and uttering it loudly is even more sinful; rather, the Sunnah is to make the intention in the heart as Allaah Knows that which is secret and what is even more hidden as Allaah Says (what means): {Say: Will you inform Allaah of your religion while Allaah knows all that is in the heavens and all that is in the earth?}[Quran 49:16] It was not confirmed that the Prophet or the Companions or any of the most prominent Imaams spoke the intention out loud. From this we understand that uttering the intention is not legislated; rather it is an innovation that has been introduced into the religion.”
So, dear questioner, you know now that Shaykh Ibn Baaz issued that Fatwa as a reply to a question about uttering the intention in the prayer and not in Hajj and ‘Umrah. Rather, the Shaykh is of the view that it is permissible to utter the intention in Hajj and ‘Umrah as per the second Fatwa to which you referred. He also said in "Majmoo’ Al-Fataawa": “It is not permissible for a person to utter his intention except when especially assuming the state of Ihraam, as it was confirmed that the Prophet did so. As regards the prayer and the Tawaaf and other acts, then one should not utter the intention in any of them.”