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]
(..) - I know that. She is here to reclaim the Iron Throne and the Seven Kingdoms. The North is one of those seven kingdoms. This isn't an invitation; it's a trap. It could be, but I don't believe Tyrion would do that. You know him. He's a good man. (..)2017 TvShow: Game of Thrones Title: Stormborn Season: 7 Episode 2