I have seen the two terms being used variously by different people.

I would assume that:

• The "Asia Pacific" relates to that part of Asia which lies in the
  Pacific Ocean. It includes regions from Russia's Pacific coast to
  ASEAN and Oceania.

• The "Indo-Pacific" is an integrated region
  that combines the Indian Ocean and the Pacific Ocean, and the land
  masses that surround them. It is Asia-Pacific plus South Asia and
  regions like Maldives and Seychelles.

I'm not sure I've got this correct.
How are the two terms "Indo-Pacific" and "Asia-Pacific" defined? Are the Middle Eastern countries also supposed to be in Indo-Pacific region? Is there some think-tank/academic organization that has defined these terms? If not, what are the "commonly accepted" definitions of the terms?

update: If no generally accepted definitions are forthcoming, is it possible to at least address When should one use "Indo-Pacific" vs "Asia-Pacific"?