Hi Greenchai,
Alain has given you the short answer, so here is the long answer:
In general the idea of there being stages on the spiritual bath is a problematic one, as the spiritual path doesn’t really have stages on it. In fact ultimately there is no spiritual path. The idea of there being a particular stage on the spiritual path is flawed on three levels: Firstly the idea of a stage exists only in the mind; secondly the idea of there being an individual person who could arrive at this stage is simply an idea in the mind; and third, the idea of there being a spiritual path in the first place is simply an idea in the mind. So, it is all based on ideas layered upon more ideas.
The spiritual path is sometimes described as being a journey from here to here. However it does not involve going anywhere else. If you try to construct a path that goes from where you are to where you are, without actually going anywhere else, you will find it is impossible.
Having said this, if we assume that it can be useful on some level talk about stages on the path from a teaching perspective, there are two AYP Lessons that talk about stages. One of them is Lesson 35 which talks about three stages on the path: The stage where bliss becomes permanent, the stage where ecstasy becomes permanent, and the stage where these two merge into divine love, unity, and liberation.
There is also Lesson 327 which talks about five stages of the mind:
These stages are pre-witnessing, witnessing, discrimination (viveka), dispassion/ renunciation (vairagya), and unity. So, it could be that the Buddhist Anagami stage correspondents loosely with the vairagya stage in AYP?
Vairāgya involves dispassion toward lesser desires and is often described as the natural letting go that comes from discovering something greater, rather than forced renunciation. When vairagya is present there is diminished attraction to sensory pleasures, freedom from reactive aversion, emotional equanimity, and actions arising more from compassion than from personal craving. Craving for sensory pleasure has fallen away in this state, and also aversion, hatred, irritation, and resentment. This is the “cessation” aspect of this stage of the path. The “insight” aspect is insight into our true nature, that we are not the body and mind, or the objects of the senses or any if the five aggregates.
A subtle sense of “I am” as a separate entity is still present, as well as subtle ignorance (ignorance of our true nature as being completely beyond all separation). This is what differentiates the stage of vairagya from the last stage, unity.
Advaita tends to be much more vague on stages of the path. The principle starting position of advaita is that everyone is already free and enlightened and if they are not aware of that it is due to ignorance which operates like clouds veiling the sun. From the sun’s perspective it is never veiled by clouds. So, there can’t be any stages. From a teaching perspective advaita teachers do talk about conditions that need to be met in order to be able to realise advaita. One of these conditions is vairagya. They also sometimes talk about path structures: Śravaṇa – hearing the teaching, Manana – reflection and clarification, and Nididhyāsana – deep contemplation / assimilation.
But they would be very unlikely to say something like “this person is at this stage” as that would imply the existence of an individual who could progress in time and achieve things, which would contradict the “everyone is always already enlightened” principle.
And yes, when monks and nuns are practicing in monasteries they can believe they are more advanced than they actually are. The conditions are deliberately set to be conducive to meditation practice and there are very few distractions. So, when they come out of the monastery they are often faced with unexpected challenges and they may not be prepared for them. And if they stop practicing, or reduce their practices below the minimum amount necessary for progress, they can fall backwards on the path which makes the potential distractions even more alluring! 