I don't own a Dinair so I'm not 100% sure but I think it is. Right now I'm using - well testing - the Luminess one. Do I recommend it? No. Not because it's bad or anything but because I can't recommend something I haven't compared to another brand.
So to answer some of your questions.
can you use any airbrush makeup in the system
Any airbrush makeup can be used in any airbrush system. I'm using Luminess' foundations along with Obsessive Compulsive's and I just ordered MAC Pro's airbrush foundations (which anyone can order over the phone from MAC or buy in a free standing MAC from what I've been told).
cant you use a regular airbrush machine with any makeup? or is it completely different???
You can but it WILL clog the airbrush unless you thin it down (I've been told how but I can't recall the product recommended to me). Airbrush foundation is very, very thin compared to normal foundation.