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]
(..) Bringing that to my table and making me dine with it? And you got what you were after, didn't you? A bastard. A half-breed bastard. Your invitation into our home. Come, my dear. Talla. I've lost my appetite. He dishonors us. You dishonor yourself. Your mother's a fine woman. (..)2016 TvShow: Game of Thrones Title: Blood of My Blood Season: 6 Episode 6