A man enters ihram for a voluntary Hajj before performing the Hajj of Islam, or enters an unspecified ihram saying "My ihram is like the ihram of so-and-so" and that person was in ihram for Hajj, so he is a pilgrim and it counts for the Hajj of Islam

Ata (may Allah have mercy on him) said: I heard Jabir bin Abdullah (may Allah be pleased with them both), among people who were with me, saying: We, the Companions of the Messenger of Allah (peace and blessings be upon him) (may Allah be pleased with them), entered ihram for Hajj alone, and the Messenger of Allah (peace and blessings be upon him) arrived in Makkah on the fourth of Dhu al-Hijjah, and he (peace and blessings be upon him) said: "Come out of ihram and have relations with the women." Ata (may Allah have mercy on him) said: He did not make relations with the women binding on them; rather, he only made it lawful. Jabir (may Allah be pleased with him) said: The news reached the Messenger of Allah (peace and blessings be upon him) that we were saying: when only five days remained between us and Arafah, he made the women lawful for us, and we will arrive at Arafah with our private parts dripping with semen. And Jabir (may Allah be pleased with him) was gesturing with his hand, as if I can still see his hand moving. So the Messenger of Allah (peace and blessings be upon him) stood up and said: "Do you know that I am the most fearful of Allah among you, the most truthful and the most righteous? Were it not for the sacrificial animal (hady), I too would come out of ihram as you do; and had I known beforehand what I came to know afterwards, I would not have brought the sacrificial animal." Jabir (may Allah be pleased with him) said: So we came out of ihram; we heard and we obeyed. Ali bin Abi Talib (may Allah be pleased with him) arrived, and the Messenger of Allah (peace and blessings be upon him) asked: "Ali! With what did you say the talbiyah?" He said: With what the Messenger of Allah (peace and blessings be upon him) said it. He (peace and blessings be upon him) said: "Then bring a sacrificial animal and remain in the state of ihram as you are." So Ali (may Allah be pleased with him) brought a sacrificial animal for him. Suraqah bin Malik (may Allah be pleased with him) asked: Is this Hajj of tamattu' of ours for this year only, or forever? He (peace and blessings be upon him) said: "No, rather it is forever."

Abu Musa (may Allah be pleased with him) said: The Messenger of Allah (peace and blessings be upon him) had sent me to Yemen, and I met him (peace and blessings be upon him) in the year in which he (peace and blessings be upon him) performed Hajj. He (peace and blessings be upon him) said to me: "O Abu Musa! What did you say when you entered ihram?" I said: I made the intention to do as the Prophet (peace and blessings be upon him) did. He (peace and blessings be upon him) asked: "Have you brought a sacrificial animal?" I said: No. He (peace and blessings be upon him) said: "Go, perform tawaf of the House (the Ka'bah) and sa'i between Safa and Marwah, then come out of ihram." So I went, performed tawaf of the House and sa'i between Safa and Marwah, then I went to some women of the family of Qays, that is, my paternal aunts, and they washed my head and combed it. Then after that, during the caliphate of Umar (may Allah be pleased with him), I came to perform Hajj. While I was telling the people what the Messenger of Allah (peace and blessings be upon him) had told me, a man came and said: Be careful with this talk of yours; do you not know what the Commander of the Believers has introduced in the rites of Hajj? So I said: O people! Whoever has heard anything, let him not act on it until the Commander of the Believers arrives; follow him. When Umar (may Allah be pleased with him) arrived, I said: Has some new ruling been issued regarding the way of Hajj? Umar (may Allah be pleased with him) became angry at this, then said: Yes; if we take the Book of Allah, Allah Almighty has commanded completion; and if we take (the Sunnah of) the Messenger of Allah (peace and blessings be upon him), he (peace and blessings be upon him) did not come out of ihram before offering the sacrifice.

(a) Sayyiduna Abu Musa (may Allah be pleased with him) said: I came to the Prophet (peace and blessings be upon him) while he had camped at al-Batha, and he said to me: "How did you say the talbiyah?" I said: 'Labbayk bi-ihlalin ka-ihlal al-Nabi' (Here I am, with an ihlal like the ihlal of the Prophet (peace and blessings be upon him)). He said: "You did well. Perform tawaf of the House and between Safa and Marwah, then come out of ihram," and he narrated the long hadith.
(b) In the narration of Tawus: The Prophet (peace and blessings be upon him) set out from Madinah without naming either Hajj or Umrah, awaiting the decision (revelation). The revelation came down to him while he (peace and blessings be upon him) was between Safa and Marwah, so he ordered those of them who had entered ihram and had no sacrificial animal with them to make it an Umrah.

Asma bint Abi Bakr (may Allah be pleased with them both) said: We set out in the state of ihram, and the Messenger of Allah (peace and blessings be upon him) said: "Whoever has a sacrificial animal with him should remain in his ihram, and whoever does not have a sacrificial animal should come out of ihram." I did not have a sacrificial animal, so I came out of ihram; and al-Zubayr (may Allah be pleased with him) had a sacrificial animal, so he did not come out of ihram. She said: I put on my clothes and went and sat beside al-Zubayr (may Allah be pleased with him). He said: Get up away from me. So I said: Are you afraid that I will leap upon you?

Ata (may Allah have mercy on him) said regarding a man who has not performed Hajj and then performs Hajj intending a voluntary Hajj, or intending Hajj on behalf of another man, or intending Hajj to fulfil his vow: this will be his obligatory Hajj. After that, if he wishes, he may perform Hajj on behalf of the man or to fulfil his vow.