I doubt that there is one comprehensive formal definition of these terms, but, in my experience, the following generally accepted definitions:
The domain is a matter of concern or, as you say, a subject. If the business is the concern, this will be the business domain. The term "problem area" is more general.
A conceptual model is an abstraction of concepts and relationships in a Domain: I would agree that the terms Domain Model and Conceptual Model are largely interchangeable. The only difference is that the term Conceptual Model emphasizes the fact that it is a conceptual model and does not reflect software design.
The terms Business Logic and Domain Logic tend to refer to rules that determine the correct behavior of objects in a domain. It may be possible to fix some of these rules in the domain model, for example, although there are restrictions on relationships or the use of state diagrams. If you think that Domain Logic is a necessary part of the domain model, it probably depends on how formal your modeling is and the domain in question.
source share