Which part are you confused on?
I think Cairns is the most common launching point to the GBR. It's fairly easy to get to and there's lots of other things to do, and lots of dive options. The area they mostly dive from Cairns on day trips or short liveaboards is called the Outer Reef. It is indeed out there a distance, but I think the name makes it sounds more remote and special than it is - it's just what that section of the reef out from Cairns is called. Sort of opposite of remote, as far as the GBR goes. There are dayboats, also liveaboards of sorts that stay out there that you can kind of treat as a hotel - stay 1 night, 2 nights, whatever. There's short 2 night liveaboards that leave from Cairns directly rather than doing transfers. I think you have to look at your flight options and timing of trips and go for the longest thing you can squeeze in. (We actually did a similar thing, squeezed a few days of diving into a business trip and were very constrained on when we could play, having lots of options is helpful.)
GBR diving gets better the further north you go from Cairns. The best bet for diving would be to take a 3 (or more
night liveaboard if you can manage it, which can get further north, or even to the Coral Sea. We did a liveaboard from Cairns, and finished up in the Outer Reef area when returning - I was not impressed. Short trips from Cairns will have you technically diving the GBR, you'll get wet and see stuff, but it might not be what you are expecting after seeing tourism pictures of what is/was probably the best of the GBR.
Also there's the whole coral bleaching thing in recent years - the area from Cairns for a good distance north was some of the hardest hit, I have no idea of the real current status of things.
Yeah, you're right, it's confusing.
If I were going there now and trying to work in a couple days of diving, I might check what is available from other towns - probably Port Douglas (perhaps SilverSonic?) , and maybe Townsville or Ayr (to dive the Yongala.) Or I'd look for an island resort with good diving (like the suggested Heron Island.) Again, you'll have to see what you can squeeze in timing-wise, may be trickier with fewer flight options to places that are less populated or less touristy.
You could go even further south, like Brisbane/Gold Coast. But it's not technically the GBR, and the water won't be as warm as you're getting into a more temperate region. (Do you have a preference on water temps?) A bit further south still is Byron Bay, which I've heard some good things about.
And if my final destination were on the west coast (you don't say where, I'm guessing Perth?) I might look into diving out there instead, supposed to be some good stuff. Perhaps Ningaloo Reef. Again, might not be quite as warm as some of the East Coast options, but depends what you want. Mostly, I would not get hung up on "diving the GBR", but on getting in the best Australian diving you can work into your travel. Might be GBR, but might not be.