Domain model-Conceptual model has different meanings in different context.
But in Object Oriented Analysis context they are same
A domain model is a visual representation of conceptual classes or real-situation objects in a domain [MO95, Fowler96]. Domain models have also been called conceptual models (the term used in the first edition of this book), domain object models, and analysis object models.[ page 134]
Source : Applying UML and Patterns - Third Edition -By Craig Larman
MO95 Martin, J., and Odell, J. 1995. Object-Oriented Methods: A Foundation. Englewood Cliffs, NJ.: Prent
Fowler96 Fowler, M. 1996. Analysis Patterns: Reusable Object Models.* Reading, MA.: Addison-Wesley