If you're looking for a definition of business communications, there's a simple answer that requires some careful consideration.
In short, business communications involve any kind of communication between a business and any other entity.
This makes the topic of business communications an enormous one, because in fact in involves media relations; every form of advertisement; every letter sent, including bills; official statements from a company; website text; even what customer service representatives say on the phone to company customers.
In other words, communications in the broadest sense involves every form of outreach from the business, which really means that it covers all areas of marketing.
I could get some arguments over that statement but, in my opinion, from those who don't think broadly enough about marketing and/or communications.
Marketing, you might say, involves market research. Communications do not. But I beg to differ. One of the primary themes to "Bottom Line Communications" as recommended on this site is that communications are not just about writing or speaking; they are also about listening and understanding. If you ever heard the phrase: "You've got two ears and one mouth -- use them in that proportion," then you get the concept here. Effective communication is never about just talking.
(By the way ... this is why "business communications" also refers to RECEIVING communications. Food for thought.)
On the other hand, it might be argued that business communications involve correspondence with other businesses (for instance), and of course that's not part of marketing. But again I beg to differ -- another point to "Bottom Line Marketing" is that EVERY form of communication is an opportunity for marketing a business. The problem, in my eyes, is that businesses often fail to look for opportunities where they assume there are none. It's my opinion that opportunity should be sought at every turn.
So as you can see, the definition of business communications is a rather simple one, but the topic as a whole is enormous. The important thing to remember is that it DOES cover every conceivable form of outreach from (and to) a business, and that outreach always has some level of effect on the bottom line.