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]
(..) 'Cause I was referring to your company's involvement in this latest atrocity. Yeah. They just put my name on the invitation. I don't know what to tell you. I actually almost bought it, hook, line and sinker. I was out of town for a couple months, in case you didn't hear. (..)2008 Iron Man