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]
(..) must come out or drown - now it's a waiting game. The rest of the pack are calling. They've made a kill in the forest and this is an invitation to join in the meal. The impala is in luck. A pack this size kills once a day and everything is shared. And this impala is reprieved. (..)2006 TvShow: Planet Earth Title: From Pole to Pole Season: 1 Episode 1