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]
(..) We will make arrests. Anyone who doesn't get the message, we'll find an answer for. What's this? A gift brought by a messenger with an invitation to meet. - Meet where? - He said you would know. Have no fear of the Zealots. They fight, they disrupt. (INDISTINCT CHATTER) (..)2016 Ben-Hur