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]
(..) that the large man in a wife-beater... sitting in front of us... invited me to the lobby to discuss your habits... and had I accepted his charming invitation... I might be in traction right now. Please, you could totally have outrun him. You're spry. Thank you. So, this is your place. (..)2004 TvShow: Gilmore Girls Title: The Nanny and the Professor Season: 4 Episode 10