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]
(..) - Yeah, my name is Chris Gardner. The message is: Thank you very much for inviting me into the program. I really appreciate it and I'd be very pleased to accept your invitation. Yes, that's it. - Okay. - Thank you. - Be careful with that. - What? (..)2006 The Pursuit of Happyness