Difference between "vanish" and "disappear"

What is the difference between these words, exactly? Both mean to stop existing or to become invisible.

vanish

He turned around and vanished into the house.

My glasses seem to have vanished.

All hopes of a peaceful settlement had now vanished.

disappear

The plane disappeared behind a cloud.

Her nervousness quickly disappeared once she was on stage.

Solution 1:

Vanish has a sense of suddenness or mystery or finality about it that disappear lacks.

In your examples, I would use "disappeared into the house." instead of "vanished into the house." The other two "vanish" examples are fine.

I think if you were to change your next example to, "The plane vanished behind a cloud." it would imply that it was never seen again. Disappeared doesn't have that sense.

In your last example, you could say "Her nervousness vanished once she was on stage."

Solution 2:

To vanish indicates:

to disappear suddenly and/or in a way that you cannot explain

and to disappear is less out of the ordinary.