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]
(..) Every Lord I've ever met it's been a cunt. Can't see why the Lord of Light should be any different. Milady. Milady. It's an invitation. To King's Landing. - Milady, you are the Lady of Winterfell. - I am. And you will represent my interest at this gathering as you see them. (..)2017 TvShow: Game of Thrones Title: Beyond the Wall Season: 7 Episode 6