What's the difference between "perchance" and "perhaps"?

I would like to know the difference between the words perchance and perhaps. I know that perchance is more literary, and a bit archaic, but that's not what I am after.

The Merriam-Webster dictionary lists perchance as a synonym of perhaps.

perchance

perhaps, possibly

The entry for perhaps.

perhaps

possibly but not certainly : maybe

I would like to know if the two words have any differences in meaning, tone, or connotation. Does perchance imply that an event is less likely than perhaps? Is the tone more wistful? Does it connote that an outcome is more desirable?

I object to people who say that “perchance” is “outdated” or “archaic”. It is a perfectly good word in modern English, but it belongs to the literary or elevated register. “Perhaps” is also not very common in colloquial speech. The vernacular equivalent is “maybe”.