This question is extremely important and worthy of reflection. In truth, this confusion is not restricted to you alone; many of those who occupy themselves with the science of ḥadīth—scholars as well as students—become entangled in this very problem. The difference, however, is that you have expressed your perplexity openly, whereas many people either do not ponder over the matter or do not feel the need to investigate and dispel the confusion.
In my view, the fundamental cause of this difficulty lies in the definition of the term ʿAzīz which is generally set forth in the later books of muṣṭalaḥ al-ḥadīth, namely that a narration is transmitted through at least two narrators. I have discussed this topic in detail in my book “Tamhīd ʿIlm al-Ḥadīth”. I would request you to study that work; in it I have examined not only the term ʿAzīz but also Mutawātir, Mashhūr and a number of other expressions together with some prevailing conceptions and misunderstandings.
At this juncture it will be appropriate first to clarify the meaning of Shāhid and Mutābiʿ; after that, once the reality of ʿAzīz has been set out, the distinction among the three will become easy to grasp.
۱۔ Definition and reality of Shāhid
By Shāhid is generally meant that narration whose matn is transmitted from one ṣaḥābī, and then the same matn—or a text conveying the same meaning—is also found transmitted from another ṣaḥābī. This second narration is called a Shāhid for the first narration.
For example, if the content of a ḥadīth is narrated from ʿAbd Allāh ibn ʿUmar, may Allah be pleased with them both, and the same content is likewise transmitted from Abū Hurayrah, may Allah be pleased with him, then the narration of the second Companion can serve as a Shāhid for the first.
In this technical usage the essential consideration is that the support for the narration comes by way of a narration transmitted from another Companion. The mere existence of multiple chains from the same Companion does not, in technical terms, fulfil the definition of Shāhid.
۲۔ Definition and reality of Mutābiʿ
Mutābiʿ is that narration or chain which corroborates a ḥadīth transmitted from the same Companion; that is, another chain is found for his narration in which both the matn and the Companion are common.
For instance, a narration is transmitted through the chain: Mālik, from Nāfiʿ, from Ibn ʿUmar, may Allah be pleased with them both; and the very same narration is also found through the chain: Layth, from Nāfiʿ, from Ibn ʿUmar, may Allah be pleased with them both. The chain of Layth will then be called a Mutābiʿ for the chain of Imām Mālik.
In this case the unity of both Companion and matn in the two chains is of fundamental importance, whilst at some point in the isnād there is a difference of narrator.
Thus the essential distinction between Shāhid and Mutābiʿ is that in Shāhid the corroboration comes by way of another Companion’s narration, whereas in Mutābiʿ a second chain is found for the narration of the same Companion.
۳۔ An important correction concerning Shāhid and Mutābiʿ
Here it is necessary to remove yet another misunderstanding. Some people imagine that as soon as a Shāhid or Mutābiʿ is found, the authenticity of the original ḥadīth is automatically established, or that by the multiplication of chains every weak narration rises to the rank of ḥasan or ṣaḥīḥ. This concept is incorrect.
The authenticity of the original ḥadīth and the finding of a Shāhid or Mutābiʿ for it are two separate matters. The presence of a Shāhid or Mutābiʿ is important in its own right, yet it is necessary to examine their soundness, the strength of their isnāds and their suitability to the original narration. A narration does not become ṣaḥīḥ merely by increasing the number of chains.
One must keep this distinction in mind also to understand the methodological approach of Imām al-Bukhārī and Imām Muslim, may Allah have mercy on them. With them, the authenticity of the original narration and the status of its supporting chains are not regarded as identical.
If the original narration is weak, the finding of some Shāhid or Mutābiʿ for it undoubtedly opens up the possibility of corroboration, yet authenticity does not follow automatically. It is necessary to see what type of weakness is involved, what is the degree of reliability in the isnād of the Shāhid or Mutābiʿ, and whether it is in fact capable of strengthening the original narration.
Some scholars become confused in this matter by the wording which Imām al-Tirmidhī employs when pronouncing judgement on a narration. I have discussed this point elsewhere; its detail is not intended here.
۴۔ The reality of ʿAzīz: a reconsideration of the prevalent definition
Ḥāfiẓ Ibn Ḥajar al-ʿAsqalānī, may Allah have mercy on him, in Nukhbat al-Fikar and its commentary Nuzhat al-Naẓar, defines ʿAzīz in these words: “wa-huwa an lā yarwiyahu aqallu min ithnayn ʿan ithnayn” – that is, ʿAzīz is the narration of which less than two narrators do not narrate from less than two (p. 47).
This definition is well known in the common books on the science of muṣṭalaḥ. Yet it needs to be pondered whether, with the early muḥaddithūn, the concept of ʿAzīz from the outset was that in every tier of the isnād there should be at least two narrators.
Imām Ibn al-Ṣalāḥ, may Allah have mercy on him, has transmitted from Ḥāfiẓ Ibn Mandah, may Allah have mercy on him, that in explaining gharib, ʿAzīz and mashhūr he says: “al-gharīb min al-ḥadīth …” – The summary of his statement is that if, in the aḥādīth of al-Zuhrī, Qatādah and the like of them among the imāms whose aḥādīth are gathered together, a single narrator alone transmits a ḥadīth from them, that ḥadīth is called gharīb; if two or three narrators share in the transmission, it is called ʿAzīz; and if a group narrates it, it is called mashhūr.
From this clarification it becomes apparent that in the division into gharīb, ʿAzīz and mashhūr it is not necessary to count the number of narrators in every tier of the isnād from beginning to end; rather, attention is paid to the number, solitude or participation of narrators at a particular point of the chain.
For example, if a narration from Imām al-Zuhrī is transmitted only by a single narrator, then, with respect to that narrator transmitting from al-Zuhrī, the narration is gharīb. If in the same narration two or three transmitters participate in narrating from al-Zuhrī, then at that juncture its character of solitude changes and the way attains the description of ʿAzīz; and if the number of narrators reaches the level of a group, it can be called mashhūr.
Here a fundamental point must be understood: the term ʿAzīz concerns the number of chains and the participation of narrators at a specific point in the isnād, whereas Shāhid and Mutābiʿ refer to the presence of another narration or another chain that supports a narration. It is precisely the neglect of this distinction which gives rise to the problem under discussion.
۵۔ Is it necessary for there to be two narrators in every tier for a narration to be ʿAzīz?
Al-Ḥākim al-Naysābūrī, may Allah have mercy on him, in Maʿrifat ʿUlūm al-Ḥadīth (p. 242) mentions two upright tābiʿūn narrating from a Companion, yet to interpret his words as laying down the compulsory condition of two narrators in every tier for a ṣaḥīḥ ḥadīth is incorrect. His purpose there is to remove the ignorance concerning the identity of a Companion, not to impose a universal requirement of two narrators for authenticity.
Among the noble Companions there are some from whom only a single narrator has transmitted, yet if their companionship is established by another reliable means and the other conditions of authenticity are fulfilled, their aḥādīth are found even in the two Ṣaḥīḥs.
Ḥāfiẓ Ibn Rajab, may Allah have mercy on him, in Sharḥ ʿIlal al-Tirmidhī, has transmitted a conversation between Yaʿqūb ibn Shaybah and Imām Yaḥyā ibn Maʿīn, may Allah have mercy on them both. From this exchange it becomes clear that the number of those who narrate from a narrator cannot be deemed the sole criterion for his recognition and the removal of anonymity; rather, the scholarly standing of those narrators and their methodological approach must also be taken into account. (Ibn Rajab: Sharḥ ʿIlal al-Tirmidhī, 377-378)
Therefore, one should not conflate the being gharīb, ʿAzīz or mashhūr of a narration with its ṣaḥḥ or ḍaʿf. These descriptions clarify one aspect of the nature of a narration, whereas the judgement of authenticity or weakness is reached through separate principles.
۶۔ The fundamental difference between ʿAzīz and Shāhid
We now turn to your original question: when two isnāds are found for a narration, why should it not be termed ʿAzīz, and what need was there thereafter to coin the separate terms Shāhid and Mutābiʿ?
The answer is that the mere presence of two chains is not in every case sufficient for a narration to be designated ʿAzīz, nor can every second chain be called a Shāhid. The distinction among these terms arises from the status in which the second chain exists and the relationship it holds with the first narration.
ʿAzīz, in contrast to gharīb, is a description in which the number of narrators and their participation at a particular point of the isnād is under consideration. Shāhid and Mutābiʿ, on the other hand, determine the capacity in which another chain is present in order to corroborate a given narration.