Pete Lacey has a post called "What is SOA?" where he defines SOA as follows:

"

• Network Oriented Computing (NOC): An approach to computing that makes business logic available over the network in a standardized and interoperable manner.
  • Service Oriented Architecture (SOA): A technical approach to NOC that has a non-uniform service interface as its principle abstraction. Today, SOAP/WS-* is the chief implementation approach.
  • Resource Oriented Architecture (ROA): A technical approach to NOC that has an addressable, stateful resource as its principle abstraction. Today, REST/HTTP is the chief implementation approach.
• Business Service Architecture (BSA): An unnecessary term (also not an architecture) that tries to make the obvious something special. Aka, business analysis. Aka, requirements gathering"

I am sorry but I beg to defer.

The first thing to note (again) is the architecture vs. architecture style differentiation I mentioned in a previous post (You can see a similar definition by Stuart Charlton) Here is a quick reminder :

Software architecture is the collection of the fundamental decisions about a software product/solution designed to meet the project's quality attribute requirements. The architecture includes the main components, their main attributes, and their collaboration (i.e. interactions and behavior) to meet the quality attributes. Architecture can and usually should be expressed in several levels of abstraction (depending on the project's size).

An Architectural style is a blue print that can be used when you desing an architecture. An architectural style defines some of the components and thier attributes as weel as place constraints on how they can interact.

My claim is that SOA is an architectural style for distributed computing which puts extra emphasis on the interface (and hence gets the easier interoperability). Ok, if SOA is indeed an architectural style, we should be able to define it as a set of components, interactions and attributes. Well, I already did that a while ago (in a paper called "What is SOA anyway?"). And while it may not be perfect, I think it is a reasonable definition all the same:

"SOA is an architectural style for building systems based on interacting coarse grained autonomous components called services. Each service expose processes and behavior through contracts, which are composed of messages at discoverable addresses called endpoints. Services’ behavior is governed by policies which can be set externally to the service itself. "

You can see the above mentioned paper for a little more detail on each of the components.

ROA, in my opinion, is just a re-branding of REST so that it would be easier to discuss it as an architectural style and not connect it to the HTTP implementation - which is what  a lot of REST proponents are doing.

By the way, as I pointed out before, there are a few other important architectural styles that are related to distributed systems like Event driven architecture, Spaced based architecture, peer-to-peer etc.

As for "Business Service Architecture" - I personally like to think about that as "SOA initiative" as in the strategic decision to try to implement an SOA in an organization while trying to achieve the more nebulous traits like business and IT alignment etc. (which is why it is nether architecture nor architecture style)