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]
(..) Needs to speak urgently about your sister's wedding. I told her you were mid-air and not even I knew your final destination. -Well done. -And you got an invitation to speak at Goalquest in Vegas. Goalquest ? Every once in a while, I do speaking engagements, motivational kind of stuff. (..)2009 Up in the Air