Database system concepts and architectures involve various data models including object-based, record-based, and physical models that describe data at different levels of abstraction. Common data models include the entity-relationship, object-oriented, hierarchical, network, and relational models. A schema defines the overall structure of a database, while an instance refers to the specific data stored in the database at a given time. Database languages like SQL are used to query, manipulate, and manage data through statements such as DDL for definitions, DML for manipulation, DCL for access control, and TCL for transactions.