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 thought I might kill someone. - You should start with your designer. Nobody wants to miss out. The notables just keep coming. Excuse me, sir. Could I see your invitation? Pete, it is okay. I am his agent. Jesus Christ, Tom. Come here. It is Tom Noonan, the actor who played the Ripper. (..)1993 Last Action Hero