She attended the fund-raiser 'at the invitation of' the committee chairperson. [=she attended because she was invited by the committee chairperson]
You have a 'standing/open invitation' [=you are always welcome; you are always invited] to visit us any time.
The event is 'by invitation only'. [=only people who have been invited to the event can attend it]
(..) There's no X-ray today. The doctor's boiling jelly. And what if he took my graceful companion with him, beautiful Bacilisu? Who here has an invitation to go to Africa? No-one, we're just chewing the fat. Wild animal paradise. And what is Bacilisu? (..)1989 Dva lidi v zoo
(..) Don't be sad, just write a letter again, and the zoo will be fine. - It would have to say something nicer. - Bugger it! - See the boss again in shorts. - With another invitation to Africa? - He'd like that. - You can't, you don't know the language. Nowhere in the world can't he express himself. (..)1989 Dva lidi v zoo