Both PyQt6 and PySide6 are Python libraries for accessing the Qt6 API, enabling the easy creation of Qt-based GUI applications in Python. The most significant difference between PyQt6 and PySide6 lies in their licensing.
PyQt6 is developed by Riverbank Computing and has been available for a longer time. It is released under the GPLv3 license and a commercial license. This means that if you use PyQt6, you must open-source your code; to keep it proprietary, you need to purchase a commercial license.
PySide6 is the official Qt library, often considered the "native" option. It appeared much later than PyQt, which is why many people are familiar with PyQt but not PySide. However, with version iterations, PySide6 has become increasingly powerful.
PySide6 is released under the LGPL license. This means that as long as you use Qt in the form of dynamically linked libraries, you can distribute your program in any form (commercial, non-commercial, open-source, or proprietary).