- The first one, which is both official and accurate, defines a set of Google services wrapped together and attached to a domain. Google Apps exists in several forms (see pricing), depending on who you are and whether you are willing to pay — the most basic form (Standard) being sometimes worse than a collection of Google regular services. Even in its most powerful edition, Google Apps Premier is not on par with Microsoft administration stack when it comes to fine-tuning deploiment. Well, at least it is not on par for the moment!
- The second definition encompasses the practice of using more than juste Google search and Gmail (personal). This is not Google Apps, but quite a lot of people (including your boss!) may think this is Google Apps. After all, from an frontend point of view, there is not much difference (from an extra hours-point of view, there might be).
At GoogleAppsManual.com, we will use both definition. The main reason is that, for a lot of companies, aggregating various services may be enough. Plus, you won't have to delve with MX migrating and redirections for special cases (lesson: there is always special case :(), especially considering that handling special case requires Google Apps Premier (wich is not free).