Database model:
A database model explains the structure/design of a database. It helps in identifying how the data is going to be stored within a database. Accessing the data is also explained within the model. It helps in defining the logical organization of the data.
Database Management System [DBMS]
A database model is implemented with the help of a database management system [DBMS]. A simple definition of the DBMS is that it helps in the interaction of the user with the database. It works with the database and the user and is collectively called a database system.