This topic will require more than one post, because there is more than one definition of "Explanation". That is, the term "Explanation" signifies more that one concept.
The first kind of explanation we will deal with can be defined as:
"Bringing a mind to an understanding of a topic".
This means that an explanation must be relative to the mind which is to be brought to the intended understanding. For instance, the way we explain the solar system to an 8-year old child will likely be different to the way we explain the solar system to a college undergraduate. The explanation offered will depend on prior knowledge, experience, developed intelligence, and probably many other factors. Differences between defintion and explanation can be summarized as follows:
- A definition is not intended to be proportional to any mind. It has to be the best description of a concept that is available. This is is quite unlike explanation, where there will be many explanations proportionate to the types of minds which are to be provided with a given explanation.
- There can be many explanations for a concept, but there should be only one definition.
- An explanation may exclude difficult points (say to convey an initial understanding), but a definition must be as complete as possible.
- An explanation may avoid technical language. A definition should aim to exclude technical language, but it may sometimes need to include technical language.
There is always a danger that an analyst creating a definition will treat it as an explanation. This will likely make the definition unusable as an authoritative reference. The analyst will probably only be guessing at the type of mind any explanation is aimed at. It is one reason careful governance of definitions is needed (so analysts do not go in the wrong direction).
It can be argued that there is an environment in which the definition is to be used, and that the definition should be the best for that environment - but might be vary across such environments. For instance, the insurance concept of "Incurred But Not Reported" can be defined within the environment of Insurance Company X, without any intent to be used in any other insurance company.
An issue here is that if a definiton is the best for a particular environment, how can this satisfy the vision of the Semantic Web which would seem to have common definitions of concepts across the entire web? However, this is an issue beyond comparing definition to explanation.