What is the difference between logical data model and conceptual data model?
These terms are unfortunately overloaded with several possible definitions. According to the ANSI-SPARC "three schema" model for instance, the Conceptual Schema or Conceptual Model consists of the set of objects in a database (tables, views, etc) in contrast to the External Schema which are the objects that users see.
In the data management professions and especially among data modellers / architects, the term Conceptual Model is frequently used to mean a semantic model whereas the term Logical Model is used to mean a preliminary or virtual database design. This is probably the usage you are most likely to come across in the workplace.
In academic usage and when describing DBMS architectures however, the Logical level means the database objects (tables, views, tables, keys, constraints, etc), as distinct from the Physical level (files, indexes, storage). To confuse things further, in the workplace the term Physical model is often used to mean the design as implemented or planned for implementation in an actual database. That may include both "physical" and "logical" level constructs (both tables and indexes for example).
When you come across any of these terms you really need to seek clarification on what is being described unless the context makes it obvious.
For a discussion of these differences, check out Data Modelling Essentials by Simsion and Witt for example.