“One‘s wish is to do something” vs “One's wish is doing something”？

Question

I can't see any difference between “His wish is to be a fighter jet pilot” and “His wish is being a fighter jet pilot”.

Answer 1

The critical difference is that wish, both verb and noun, licenses infinitival complements but does not license gerund complements:

^okI wish to go.
^∗  I wish going.

"His wish is being ..." is not idiomatic.