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]
(..) the act of deserting is a heroic one. Shall we go? What else can i do? A romance, Mr doctor? I don't have the voice. I prefer wine. Thank you for the invitation. I hope that tomorrow they are going to use me for something. What is this? I was told that over here the atmosphere is calm. Nothing... (..)1965 Forest of the Hanged