I do not understand the difference between PostGIS and PostgreSQL.
What is the difference in detail between them?
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PostgreSQL is an object-relational database management system. In other words, it is software that allows you to manage databases. By default, it does not manage spatial data. In order to work with spatial data it is necessary to install a module named PostGIS. Therefore PostGIS is the module of PostgreSQL that allows you to work in GIS.
As one might expect, the PostGIS website itself offers a multitude of explanations. Emphases below are mine.
Spatial and Geographic Objects for PostgreSQL
PostGIS is a spatial database extender for PostgreSQL object-relational database. It adds support for geographic objects allowing location queries to be run in SQL.
PostGIS is an extension to the PostgreSQL object-relational database system which allows GIS (Geographic Information Systems) objects to be stored in the database. PostGIS includes support for GiST-based R-Tree spatial indexes, and functions for analysis and processing of GIS objects.