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]
(..) Have fun. Thank you. Sit down. Life is really incredible. Cecilia chose the menu. She even did the invitations. She just forgot to come. To the President! - To victory! - Cheers. Have fun. For two hours now Nicolas Sarkozy has been inside. (..)2016 Me Before You