From a figure of authority the question may amount to the same thing, for the student is probably not allowed to be finished with their homework until it is finished.
This is probably true, and illustrates the value of a pragmatic approach to these questions in ESL/EFL classes. But this...
"Have you finished" is a question about the homework. "Are you finished with" is a question about the person. The contexts may be imagined accordingly.
...is not true, I'm afraid,
woodcutter. It's tempting to think about them that way, I'll admit, but your statement doesn't hold up to scrutiny.
To make them easier to examine, convert both from questions to statements, using the "move the first auxiliary" rule. Then you have:
you are finished...
and
you have finished...
The subject is "
you", and not "
homework" in both cases. So it appears both sentences are about "
you." Only one difference can be seen, which is the difference between the effect of "
are" in the first case, and "
have" in the second. As I've mentioned before, I believe the first of these two is an unmarked, present simple, fact only statement. No issue of time is undertaken in that case. The second sentence contains a verb phrase including the auxiliary "
have" together with a past participle verb form, making it a present perfect verb phrase. That, to me, means that not only is a fact stated, but also a temporal element asserting that the homework is "finished" before the present moment.
Please forgive my pedantic, academic focus here. I don't mean to display any kind of "attitude." But since we are teachers here, there are sometimes technical points at issue. I believe there is a technical error in your statement,
woodcutter, and merely want to explain clearly why I think so.
Larry Latham