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]
(..) ls it silk? ls it plastic? I know it all seems a bit much... ...but how else was I going to meet you, Superman? I knew you'd never accept an invitation to tea. But a disaster, with people in danger, people who needhelp.... I just knew you couldn't resist that chance to sort of pitch in. (..)1978 Superman