According to wikipedia they seem to be the same thing, but they each have different pages.
On the conceptual model page it says these two things:
A Conceptual model in the field of computer science is also known as a domain model.
a conceptual model represents 'concepts' (entities) and relationships between them.
But on the domain model page it says
A domain model in problem solving and software engineering is a conceptual model of all the topics related to a specific problem. It describes the various entities, their attributes, roles, and relationships, plus the constraints that govern the problem domain.
Are they actually the exact same thing?