Yes - the difference is not one of grammar but the meaning being conveyed. 'can' is used to indicate that something is typically the case : "Antique clocks can seem out of place in modern homes."
"He could be very moody."
and so, "He can be difficult at times". - This child is what we call 'a handful' - someone difficult to deal with or keep under control.
'may' and 'might' are used when there is less possibility, less certainty.
So, "He may be difficult at times" means that the teacher of this pupil might be lucky and he'll be an angel, but watch out, there may be the odd occasional day when he's a regular devil.
"We may go to the movies later on." The listener would be optimistic, chances are we'll be going to the movies.
"We might go to the movies later on." It's one possibility...I don't want to dash your hopes outright and tell you it's unlikely, ((but yes, it is far less likely there will be any movie he'll be watching today!))
In asking questions eg
"Can I ask, when you were talking about the war, you seemed to indicate..."
"May I ask, when you were talking about the war, you seemed to indicate..."
The difference is purely that the use of 'may' is more polite, less of a brunt approach to asking a question. It's almost like saying, " I hope you don't mind my asking, but..."
We can/could go to the movies later on' would mean a suggestion, wouldn't it?
Look, we just don't have time today. We can go to a movie tomorrow.
I know you're disappointed, but we can go to a movie tomorrow.
Both imply that time-wise, going to the movies is a definite possibility the next day.
We could go to the movies later on.
This is making a suggestion. It implies, 'or we could do something else if you'd prefer.' It invites the listener to then give his opinion.
. In my language, we can ask something like 'Where can those glasses be' , expressing annoyance, because we really need them. What would you say? Is 'can' totally out of place here?
Yes, someone would say with the same sense of annoyance, "Where can those glasses be?" and
She: I've looked all over the house and still can't find my glasses.
He: Well, think, where else could they be? You went over to Susan's this morning. Could you have left them there? He is asking in all seriousness, trying to be helpful.
"I've looked all over the house and still can't find them. But where else could they be? A great emphasis on the 'could' and tone of voice would convey that despite not being able to find them in the house, the person adamantly believes they must be there somewhere in the house. It seems so unlikely that they could be any other place. It's like the person would be sceptical of any other possibility.
2.Can you tell me if you feel there is any difference between could and may, or could and might in expressing this 'weak' possibility?
'He could be very moody' - can this refer to the present?
Unsure. Take this sentence: " Thank God he's no longer a teenager. He could be very moody. He's really grown up to be a very agreeable person."
"Oh, I haven't seen John for years. How is he? As I recall, he could be very moody at times."
All the sentence 'could be very moody' tells us is about his behaviour in the past. Moreover, we don't know whether the person means he was moody for an hour, a day, or weeks at a time. In other words, we need a lot more conversation to clarify this. If so, does it sound more like 'He can be very moody' or 'He may be very moody'
or 'He might be very moody'???
Imagine, a parent is leaving his child with a particular child-minder for the first time, and says:
"Johnny can be quite difficult at times." That is, he has been known to be difficult in his behaviour in the past. He may be as good as gold today, but be warned in case. Also, "at times" might imply the over the course of a morning, or a day, there may be just instances of "difficult behaviour" punctuating a general cooperativeness; or that when the mood is on him he's a terror all day. This would be elaborated and clarified in further conversation between them.
"Johnny could be quite difficult at times." Generally, he was well-behaved, but occasionally in the past he had his 'off' days/moments.
"Johnny may be/could be difficult today. He's been in a bad mood all morning." Expect the worst - it's highly likely there are going to be tantrums. Both are equally 'weak' here, as opposed to saying, He will be/he's going to be a handful today...
"Johnny might be quite difficult today." With this way of expressing it, in this context, there is also a subtlety of communication going on. Yes, it can be taken to imply that there's the odd chance he may be difficult today. However, there is a second possibility as to why the parent has phrased it this way. Imagine the parent knows full well Johnny's going to give this child-minder hell. the parent is not going to say that straight out. She might be scared off and decline to sit for me. So he kind of gently prepare her instead, understating the possibility, but still giving her a degree of forewarning.