Thanks for the answer.
Still, it just seems that if the Inner Planes were the same between Athas and the rest of the Great Wheel, the contacts between the two should have been much more common, as any travel to any Inner Plane would bypass the Grey or whatever other barriers there were between Dark Sun and the rest of the Great Wheel. Also, how are the differences in paraelemental and quasielemental planes explained?
Well, this is a fair point, and one I didn't delve into too deeply above. Simply put, although there are enough points of correspondence between Planescape inner planes and those of Dark Sun to assume that they are the same, at the same time there are enough points of difference to raise questions of their differences.
The DS inner planes differ from those of the Great Wheel in a few ways, not least of which is nomenclature. Yes, DS has planes of Earth, Air, Fire and Water. But it also has Silt, Sun, Rain and Magma paraelemental planes. While Magma corresponds easily to the Great Wheel plane of the same name, the others are less easy to link. Sun exists through a confluence of Fire and Air, so you could equate that to the Great Wheel plane that lies in the same position, for example (is it Smoke? can't recall...) But its characteristics don't quite match those of the Great Wheel, so you could also argue that equating the two isn't such a good idea.
Different fans have addressed this in different ways. An easy solution is to say that the DS Inner Planes aren't the same as those of the Great Wheel, and that any seeming similarities are just coincidences (although this doesn't fully explain the gate from the Great Wheel plane of Fire to Athas). Another approach is to say that the DS inner planes are regions of the Great Wheel inner planes that are generally unknown to planewalkers for whatever reason - and vice versa. Or you could say that Athas lies in the far future of the multiverse, and that the Great Wheel inner planes eventually devolve into those seen in the Dark Sun setting (I use an approach similar to this myself). Without any solid answer, you have a great deal of freedom in how you choose to address the issue.
Additionally, there is also the issue of the wars between the elements that is a part of the DS setting. DS lore depicts the elements as perpetually battling one another, with the conditions on Athas being caused by and in turn influencing the state of the planes. So Silt is defeating Water, with obvious results, for example. There are inter-elemental conflicts in the Great Wheel, but it seems less apocalyptic than in DS, and has less effects on the Prime Plane (afaik - others may correct me on this).
So, this is a comprehensive list of connections mentioned so far between Athas and the Great Wheel:
Planar Gate (artifact in Dregoth's possession)
?Athas-Elemental Plane of Fire portal?
?Common Inner Planes?
There is also the githyanki gate to the Astral from Black Spine
and a handful of summoning spells and items. I wouldn't go on record as saying that this is a 100% comprehensive list, but it's a good overview. There should be a few more tidbits forthcoming from Athas.org in the next few months, as they are releasing some previously unpublished TSR-era materials that deal with planar connections here and there (specifically, the Secrets of the Dead Lands
and the Faces of the Far North
and Lost Cities
publications). These are still in the final phases of development, though, so I'm not really at liberty to discuss more until the finished products are released.