Does that really count as 2 sites? Did you have to buy them separately?

yes they are two different sites in the eyes of search engines due to different domain names

Terminology matters.

In the example offered up there is one domain:
-- xyz.com

... and two hosts (or hostnames):
-- xyz.com
-- a.xyz.com

The search engines don't treat these two hosts differently becasue they are two hosts. The search engines can, and do, choose to treat them however theey want to treat them. Indeed, the way that they treat them has evolved over time. Google for example not long ago changed in some significant respects the way they treat subdomains.

It's a fair generalization to say that in some respects subdomains are treated as "different Web sites" and in some respects more like part of the main site.

As for the original question, very general questions tend get little response from members, especially if the answers are easily available by searching or surfing the Web. ;-)

In this case, it is not difficult to go out and see that subdomains link back to the main host all the time, and vice versa. But so what? What you really want to try and understand is the exact nature of the linking patterns used at different kinds and sizes of sites. And the best way to understand that is to go look for yourself. All the forum feedback in the world is no substitute for personal observation.

last time i talked to matt cutts about this subject just over a year ago, he indicated that in most cases there was little inherent difference between a subdomain and a subdirectory.
here is his contemporaneous blog post on subdomains and subdirectories [mattcutts.com].
i would stay away from subdomains unless there is a significant amount of content for that subdomain that is irrelevant to the primary domain.