Are ahadith generally considered to be paraphrased?

Question

While there are different readings of the Qur'an (see What are the readings (qira'at) of Quran? and Examples of verses of the Qur'an with two different readings?), they are consistent with one another to a high degree.

However, I have not encountered the same level of accuracy with ahadith. Indeed, different books report the same hadith differently, and indeed, there are differing version of ahadith within single books. This gives the impression that ahadith should be regarded as only an approximation of what the Prophet actually said/did, and that there's going to be substantial (possibly unrecorded) inaccuracies.

Question: Are ahadith generally considered to be paraphrased?

As a concrete example, consider the following ahadith about women travelling alone:

It was narrated from Abu Sa’eed that the Messenger of Allah (ﷺ) said: “No woman should travel the distance of three days or more, unless she is with her father, brother, son, husband or a Mahram.” -- Sunan Ibn Majah [grade: sahih] (sunnah.com)

Narrated Ibn `Abbas: The Prophet (ﷺ) said, "A woman should not travel except with a Dhu-Mahram (her husband or a man with whom that woman cannot marry at all according to the Islamic Jurisprudence), and no man may visit her except in the presence of a Dhu-Mahram." A man got up and said, "O Allah's Messenger (ﷺ)! I intend to go to such and such an army and my wife wants to perform Hajj." The Prophet (ﷺ) said (to him), "Go along with her (to Hajj). -- Sahih al-Bukhari 1862 (sunnah.com)

Narrated Ibn `Umar: The Prophet (ﷺ) said, "A woman should not travel for more than three days except with a Dhi-Mahram." -- Sahih al-Bukhari 1087 (sunnah.com)

Ibn 'Abbas (May Allah be pleased with them) reported: The Prophet (ﷺ) said, "No man must not be alone with a woman except in the presence of her (Mahram). No woman should travel except in company of a (Mahram)." A man said: "O Messenger of Allah! I have been enrolled for such and such expedition, and my wife left for Hajj." He (ﷺ) said to him, "Go and perform Hajj with your wife." [Al- Bukhari and Muslim]. -- Riyad as-Salihin (sunnah.com)

Qaza'ah reported: I heard a hadith from Abu Sa'id (Allah be pleased with him) and it impressed me (very much), so I said to him: Did you hear it (yourself) from Allah's Messenger (ﷺ)? Thereupon he said: (Can) I speak of anything about Allah's Messenger (ﷺ) which I did not bear? He said: I heard Allah's Messenger (ﷺ) saying: Do not set out on a journey (for religious devotion) but for the three mosques-for this mosque of mine (at Medina) the Sacred Mosque (at Mecca), and the Mosque al-Aqsa (Bait al-Maqdis), and I heard him saying also: A woman should not travel for two days duration, but only when there is a Mahram with her or her husband. -- Sahih Muslim 827 d (sunnah.com)

With other versions here and here.

These are all simultaneously regarded as "sahih", yet are inconsistent with one another in a non-trivial way, i.e., the meaning changes hadith to hadith. As such, it seems reasonable to believe that they're all paraphrased to some degree, i.e., they're not all word-for-word identical to what the Prophet said.

Answer 1

They are not suppose to be. But they will be to some extent. Why? Have you ever played the telephone game? Also they didn't have a computer that would underline grammatical mistakes for them. Computers were invented later.

People used to memorize narrations more than they wrote them. Most Islamic books were wrote a 1-2 centuries after the prophet. In addition in the early days Arabic was usually written without dots. (I'm sure there were other things that some decided not to do—which created confusion. They didn't have standards on how to quote/write. Those standards were later built by groups)

Sometimes there were 7-8 people in the the room and then all heard something slightly different.

Having that said if a narrator heard something, even if it was confusing to them, their job was to write it down as they heard. But add a footnote explaining why they think the narration was to be written differently. (Sometimes their job is to completely refute a false narration ( Sometimes there were narrators who didn't like what they heard so they changed the narration or made up a narration of their own, even in today's world where there are numerous fact checking ways, people still lie and get away with it. Back then it there was no CNN fact checks). How do they do that? They apply the narration against Quran and if Quran doesn't approve it they may refute its authenticity. Or if the chain of narrators is not a reliable one or if the great majority of narrations are conflicting with it or a mix of all these. But a scholar would/does take extreme caution when doing so.)

Conclusion:

Their duty is to copy + paste or refute or copy/paste but add footnote.

Their duty isn't to copy + paraphrase to what makes the most sense -> paste.