Can I use categories to determine where something is posted?

Have you read over the Category Templates article in the codex? Is that the direction you’re looking to go in?

Good luck,
Michael.

That’s not exactly what I am looking for. Basically , I want to have two pages on my site News and Correspondence, to list the posts that go into those separate categories. It would be as if there were two separate blogs.

What exactly is that ‘doesn work out well’?
If I understand correctly what you said – your structure is like:
a static homepage (page by one of the many plugins or otherwise)
category templates (like category-1.php for news and category-2.php for the other one
they are styled differently in the stylesheet – and the listings of these categories (aka catgeory “archives”) show up nicely displayed using these template files

Of course, (and this is the bit nobody ever reads in the Codex) these catgeory templates do NOT apply for displaying single posts from any of the categories. For this, you should use a plugin.

After thinking about it, it seems as though I should go ahead and do two completely separate blogs, instead of trying to separate the topics by category. If I use one of the multiple blog plugins, can I also use the static homepage plug in?

What is the multiple blog plugin?

I don’t know which one will work the best with the static homepage plugin. But here’s another question: The static homepage plugin site says to create a category called blog in order to have the blog page, but what if i want to have the blog be called news?

Maybe there are other homepage plugins that dont’ demand that. They might even be better ones… (I find that requirement silly, but that’s strictly my personal opinion!)
Plugins

EDIT. Does the scenario I described above fit what you’d like to achieve?
The more details you give about your goals the easier is to find the solution.
Did you site down and make a diagram/chart of your site’s structure? Know what you want and then find the tool…

Basically, I don’t want the website to look like a blog, even though the news and correspondence sections clearly are. So, I think that I need to put two separate versions of “the loop” into my news and correspondence pages. I don’t know if this is possible yet. Obviously the news page should only display posts from the news category and the correspondence page should only display correspondence posts.

I know this seems weird, but I am just trying to harness the the power of blogposting in order to make a site that is easy to update (as it is for my boss, who is not into coding and whatnot).

This seems to be pretty simple.
The “not-blog-like” look can be achieved with a static frontpage (or using a home.php in your theme).
If you have 2 links on that frontpage to the 2 categories – clicking on those will take you to the category listings (or archives) view which displays only posts in that category.
I don’t see any complication here…