I don’t believe I’ve heard “might” used for the permissive sense of “may.”
I also believe “might” is functionally past tense, in the same sense that could and would are the past tense of can and will, respectively. If I say “I may have gone,” that means the option still exists that I did go. If I say “I might have gone,” that communicates that I didn’t, e.g. “I might have gone, had somethinge else not come up.”
Without words like “have,” I would agree the conditional sense allows both words. However, I would get a possible implied negation out of “They might be giants” but not “They may be giants.”
What? No. Not at all. It might rain in either case.
If you see someone who looks tall in the distance, you could say “They might be giants, or those might be small houses.” If somebody has twins who are like, massive babies, you could say “they may (in the future) be giants.”
I’m not sure I understand the question, since the band name doesn’t have to make sense or anything.
“May” indicates that you are more likely to do something. I may go to the store means I probably will go to the store. “Might” suggests that you are less likely to do something. I might go to the store means it’s unlikely that I’ll go to the store. So while I may dance the hokey pokey with my daughters tonight (something we do most nights), I might hang up my clean clothes in my closet (something my wife claims I haven’t accomplished in five years).
I do not believe that are always precisely interchangeable. (Also considering ‘might’ as the past, possibly subjunctive, tense of ‘may’.) It also depends on precisely what is meant: it is possible that they be giants? It is possible that they are giants? They would be giants, if not for…?
ETA it is a complete sentence, but what can it mean?
In the case of “They might be giants” it is referring to the remote chance that a windmill is actually a giant, as opposed to a more likely misidentification: “They may be ship sails.”
While I certainly won’t disagree, you have to be prepared to deal with the situation that they might be fake or they might be lies. Or, they might be big, big, fake, fake lies.
Whilst I think these words probably had distinct meanings in the past, now, they’re pretty much in the ‘use whichever one feels right’ category - and ‘feels right’ might not be the same for the writer/speaker as it is for the reader/listener.
If I’m looking out of the window at clouds gathering, I’ll probably say ‘It might rain’.
If I’m planning an event in April, I could choose to say ‘It may be raining’ (or ‘It may rain’)
Years ago, the lobby of a concert hall in my area had a prominent sign that read LATECOMERS MIGHT NOT BE SEATED. I always assumed they went with “might” instead of the (IMHO) more natural-sounding “may” because LATECOMERS MAY NOT BE SEATED could be misinterpreted as “No latecomer is allowed to be seated.”
I gave up on may vs might some time ago after being roundly informed that I was being pedantic in wondering why bridges were given permission to be icy.