Business models are designed to capture specifics and to enforce consistency. Having consistent content is important in a multi-user environment. Consistency will make it much easier for you (and your teammates) to search for and find content in the future. Consistency is enforced by rules contained within the selected catalog. These rules often restrict the user from adding content that does not make sense and limits them to the types of concepts and relationships they can add.
Another important difference is that the content added to a Business Model becomes instantly available to others within the same domain. Business Models make up your team's knowledge base and therefore should contain content that is as detailed as possible.
Concept Models are flexible and designed for capturing ideas. These models are not shared with anyone by default and typically do not enforce consistency rules. Users are free to be as detailed as they wish. Often users will begin to document a complex process with a Concept Model when they lack the detail necessary to use a Business Model.
An example of a Concept Model: