I can only speculate why the main body of the site and the support area were set up separately, as that happened before I came on board.
I think it was because the main part of the site was being maintained by an outside company (I was the first in-house webmaster here), while the support area was running on a custom content management system that had been developed by an in-house programmer. This was 10+ years ago, before everybody started using WordPress for everything.
So, initially I think it was simply done for ease of administration. With everything already in place and no compelling reason to change, it has simply stayed that way over the years.
It actually has worked out to our benefit from time to time -- for instance, when the "main" section of the site was hacked recently, the support area and the "store" were both unaffected and continued to operate without a hitch. We actually made a bunch of sales while the main part of the site was still messed up, because the store pages show up well in search results and the store was fully functional.
As to why the store is separated, again that was for site administration reasons.
At the time, the main and support sections of the site were hosted on a server sitting in a closet in our building. Management's original plan had been to run the store off the same server. Both the IT manager and I were adamant that we were not equipped to run an ecommerce site in-house. We don't have a true "data center" (no redundancy, no back up generator, etc.) nor are we staffed with security experts, nor are we open 24 hours a day -- storing credit card information locally would essentially paint a big ol' target on the side of our building and we'd be leaving the place unguarded every night, weekend and holiday. Software security can only get you so far. You need people watching, too.
So we insisted that the store be externally hosted.
We could have done it with a subdomain, of course, and I honestly don't remember why we decided to go with a separate domain instead, but either way the effect would have been the same. The store was originally hosted externally in a secure datacenter, while the rest of the site was hosted internally. And the store was running a completely separate stand-alone ecommerce/store/cart software that has nothing to do with the software serving up the rest of the site.
Eventually, of course, I migrated all our websites to the external host, so we don't run any internal web server any more. But each domain sits on its own independent software. In some cases, individual pages within a domain are running their own separate scripts. It works with our business organization -- making it easier for me to grant access to other employees only to those sections of the site they need, and to keep them out of areas they shouldn't be messing with. It allows me to offer better-quality functionality to our visitors. (I can select a script based on it's individual features and quality, rather than having to settle for what's available as an add-on to an existing content management system.) Otherwise, we'd need a custom-written CMS.
It sounds complicated when I describe it, but once one sees it in action, one comes to understand it actually makes pretty good sense from a business management point of view -- and it's a lot easier to administer than it might seem at first glance.
And qwerty is right -- it doesn't matter how you divide up the site. It's OK to split things up however you want. In fact, you could put every page of your site on a different domain if you wanted to. Personally, I think that would be weird, and it would almost certainly be an administrative nightmare, but if you could if you wanted to.