'Clairvoyance' implies clear-seeing - and usually means perceiving that which is normally unseen; and it can include being a 'seer' - who can more clearly perceive the future. (I am using the term clairvoyance to include all kinds of perceived experiences - seeing visions, hearing voices, performing divination etc.).
'Seeing' more generally implies perception, and this reflects that clairvoyant-type experiences are necessarily at several removes from reality, indirect.
In this respect 'clairvoyance' - perhaps surprisingly - can be seen as typical of all the normal, everyday, indirect - including 'official' - forms of knowing.
Intuition, by contrast, is direct-knowing of the primary level of reality.
Therefore, intuition (in its pure form) must not include anything that renders experience indirect or mediated; e.g. no language or symbolism, nor translation, nor interpretation.
In this respect intuition (in its essential, original, private form*) can be regarded as categorically different from any other kind of knowing.
I believe that intuition can best be understood as Primary Thinking; when Thinking is itself the 'primary' (ultimate) reality: such that God and creation are to be understood as (primarily) Thinking.
This means that when we engage in Primary Thinking, we are directly participating-in ultimate reality.
There is no 'mediation' - such that in Primary Thinking (and only in PT) we are part-of the ultimate reality of things.
This means that clairvoyance - because it includes perceptions - is at several removes from reality.
1. If Primary Thinking is ultimate reality...
2. Reality needs to be translated into symbolism, such as language...
3. This symbolism needs to be communicated, transmitted...
4. The received communication needs to be interpreted and understood.
This same, multi-layered indirectness (selectivity, summary, hence distortion) implies to all external sources that are received by the senses - even when it is assumed that the external source is working honestly on the basis of valid knowledge of reality.
This constraint applies to external personal and institutional authority, to all written (and spoken, and visual) inputs, to all socialization, training, education...
In sum - the above explains why we must ultimately, at the deepest and foundational level of knowledge of reality level know for ourselves.
No form of external and indirect knowledge can substitute:
We must do Primary Thinking for ourselves - or it will not be done; and we cannot be grounded in knowledge of reality.
We must do Primary Thinking for ourselves if we want a direct relationship with the world; yet there is no 'method' for doing it; and many or most people probably assume that they cannot do it - and have no idea how to start...
There is no 'method' for Primary Thinking - but there is a 'framework' of sorts; various 'assumptions' which enable Primary Thinking to happen.
For example: to know that Primary Thinking is both real and possible, both necessary and a Good Thing. To knowing that this is a creation we inhabit; that God is the creator; and that God loves us each as his child and desires our salvation - and will therefore ensure that anything we need in this mortal life will be possible.
And then by wanting to do it: by wanting to know the truth of things, wanting to experience reality - and wanting to participate in reality by Primary Thinking.
If, then, we experience what seems (on reflection and examination) be be Primary Thinking, then we would be wise to regard it as true (unless or until further intuition modifies it) - because there is no comparably valid source.
Yet (again I emphasize) we cannot communicate the results of intuition to others, nor should we expect others to be bound by our own Primary Thinking; and in general this 'trying to convince others' ought not to be attempted because public discourse can only use public language/ symbolism/ imagery etc.
On the other hand, intuitive knowing can and should affect public discourse indirectly; as the most important influence for an individual on evaluating public knowledge claims, and discerning between rival claims.
And - insofar as a intuitions is a valid participation in reality; then another-person's intuition of the same part-of-reality (if indeed, it is the identical part-of-reality that is being considered) will be the same insight - albeit within constraints of ability, time, effort etc.
But this is only true when mortal Men are living as-if already in Heaven.
*Note: The commonest criticisms of intuition come from those who focus on secondary and indirect communications of the (alleged) experience of intuition - in other words, the criticisms are directed against those who are regarded as arguing that 'other people' should accept as valid, linguistic interpretations and summaries of experiences that were originally wordless and private.