No. Not OK

Hmm just read on another site on the internet that it's fine. ?!

SOH, so you be the judge, but it would appear that an island hood is finished on 4 sides and a wall hood is finished on 3 sides so one side can be mounted to the wall. Rather depends on what style you have selected.

Ok that may be the difference one I'm referring to is out of ceiling

I am trying to figure out why you would buy an island hood, which is more expensive ,for a wall install