The Component and Deployment views came straight from the UML standard. The Conceptual view followed somewhat from this Wikipedia definition, but extended beyond the entity-relationship domain to include processes in something of a data flow. The Contextual view was used to describe the surrounding business processes, actors, and external systems that interacted with the application or system being described.
It was a challenging exercise to work through the application systems that I was responsible for and document them appropriately, without overdoing the documentation. Personally, I found the exercise very satisfying. It helped me prove out my understanding of the systems I worked with. Often, I'd start with a middle-layer view, like the Conceptual or Component view, then work my way either down or up, iterating back and forth a few times to make sure the depictions remained consistent, honest, and valuable.
As a side note, that sort of iterative process of working non-linearly, both up and down between different levels of abstraction reminds me a lot of the YouTube videos I watched a while back when learning how to use an abacus. If you aren't familiar with how to use an abacus for simple math, take a look. If you're trained in traditional Western math, it'll be an eye-opener.When introducing the idea of these four views to subsequent teams, one of the biggest surprises has been the level of dishonesty that tends to appear in the higher levels of abstraction. I've also found it hard to explain what it means to be dishonest about an abstract view of something.
For instance, in a Conceptual view, I've seen people draw a box that is intended to represent one conceptual system when the box actually comprises two or more entirely independent processes. For example, by this definition, it would be dishonest to diagram a single box labeled Item Master that has arrows sending data to separate operational systems if there is, in fact, no system or business process that actually manages a conceptually unified source for the item information in those systems. Not that there has to be some physical thing or even one single source of truth, but if the item information is built separately in those two systems with no regard for the the other system, then it would be disingenuous to suggest there's even a conceptual idea of a single Item Master. That's not to say that there should or shouldn't be -- but to document a conceptual view of that in the current state would be dishonest.
It's a lot like scientific mathematics 101. Remember the lessons about significant digits and the difference between precision and accuracy? Precision defines the degree of specificity and detail to which the answer is given. A component diagram is more specific about the actual construction and inner workings of a system than is a conceptual diagram. In order for them to be correct, both must be highly accurate depictions, though. Losing accuracy during abstraction will only get you in trouble.