Difference between "may" and "might"

Is there any difference when used in conditionals or hypothetically? Michael Swan, in his grammar, claims "may" suggests something is more likely compared to "might". Is it really perceived that way by native speakers, or are they just the same and "might" is just more common and informal?

It's dangerous to stay here. The building may collapse.
It's dangerous to stay here. The building might collapse.

Most of the time, the two are interchangeable. Judging the likelihood of an event tends to be pretty subjective, so no one's going to stop you and say, 'No, it's more likely than might. You should say may.' But, we can also use may exclusively to let people know that they are allowed to do something. 'You may sit down now.'

It is correct to say that today they are practically interchangeable.

But from a historical, and perhaps slightly prescriptivist perspective, an analogy can be drawn between 'may' and 'can' in regards to 'might' and 'could'

It's dangerous to stay here. The building may collapse.
It's dangerous to stay here. The building might collapse.

confer:
It's dangerous to stay here. The building can collapse.
It's dangerous to stay here. The building could collapse.

although it is not generally seen as being so clear cut today, the forms, however, are meant to be one-for-one

The traditional distinction is that "may" indicates" being allowed, while "might" indicates possibility. "Students may turn their assignments in tomorrow" means that they will not get marked down if they turn their assignments in tomorrow. "Students might turn their assignments in tomorrow" means that it's possible that they could do so. Sometimes, "may" is used for possibility, but that is frowned upon by some (and can lead to confusion if the audience thinks that you mean permission). And "might" always means possibility.

<<The traditional distinction is that "may" indicates" being allowed, while "might" indicates possibility.>>

Hmmm. This 'may' or 'may' not be true :\

Truth be told, "may" can mean several things: possibility, permission, opportunity, contingency, desire, ability, ..., but 'might' is the past tense (both indicative and subjunctive) of 'may'

For all I know, when "may" and "might" refer to possibility, "might" simply suggests it's even less likely to happen.

On the other hand, using what Leasnam said, in this example:

- "can" here would refer to ability,
states that the building is able to collapse thanks to the structure etc "It can collapse"="It's able to collapse", "It may collapse"
- "could" would refer to possibility,
like saying "It could even collapse" is like" "Let's get out of here, it might collapse" (=very likely)

So it's just a contradiciton of what I was tought and what I just learned from Leasnam -helpful


And what about "You might want to switch it off first." ? Which means something like "You'd better do so".
Can you use may instead? (interchangeability)

<<On the other hand, using what Leasnam said, in this example:>>

You're not using what I said. You've got it all mixed up, fella.

<<So it's just a contradiciton of what I was tought and what I just learned from Leasnam -helpful >>
Ahhhh--sweet sarcasm. doesn't bother me none. I Love it!

Hey, I did not mean it sarcastically at all,
I was trying to figure out how all this is, I'm sorry to hear I got this all mixed up.
So I'm quite confused

(btw I mistyped "taught" before)

<<Hey, I did not mean it sarcastically at all,
I was trying to figure out how all this is, I'm sorry to hear I got this all mixed up.
So I'm quite confused
>>

Oh, sorry man, my bad :)