What is the difference between logical data model and conceptual data model?
First of all, a data model is an abstraction tool and a database model (or scheme/diagramm) is a modeling result.
Conceptual data model is DBMS-independent and covers functional/domain design area. The most known conceptual data model is "Entity-Relationship". Normally, you can reuse the conceptual scheme to produce different logical schemes not only relational.
Logical data model is intended to be implemented by some DBMS and corresponds mostly to the conceptual level of ANSI/SPARC architecture (proposed in 1975); this point gives some collisions of terminology. Zachman Framework tried to resolve this kind of collision ten years later introducing conceptual, logical and physical models.
There are many logical data models, and the most known is relational one.
So main differences of conceptual data model are the focusing on the domain and DBMS-independence whereas logical data model is the most abstract level of concrete DBMS you plan to use. Note that contemporary DBMS support several logical models at the same time.
You can also have a look to my book and to the article for more details.