Arrival a bit late ...
I see the database as a special type of data warehouse. The data warehouse, as the name indicates, is the place where the data is stored.
You can store data on your hard drive using a file storage system (for example, ext4 on Linux) or in a database (for example, PostgreSQL), in which data is stored in files, but these files are managed by a control system database (access permissions, unique keys etc.).
NoSQL databases usually do not have a built-in manager, so management is done at the application level. You can consider them as a storage system.
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