"Static" means support for PostgreSQL will be built into Qt library and every Qt program using the SQL module regardless if it communicates with PostgreSQL databases or not will need psql library. This is not the case with plugins. Therefore if you want to develop different kinds of applications with Qt, it's better to use the plugin approach. Just remember that if you build Qt statically, plugins will also be built statically (although not as part of Qt library) and you will have to tell your program to link against specific plugins (see docs entry for "static plugins").
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