Connecting USB 3.1 front panel to USB 3.2 motherboard connector

As far as I know there exists only three different USB connectors for mainboards:

  1. USB 2.0 connector
  2. Connector for "USB 3.0" (also labeled USB 3.0 in your first picture).
  3. Connector for USB-C (named USB 3.1 Type-C" in your first picture).

Your confusion is caused by USB-IF which has renamed the USB standards several times so that USB 3.0 is also known as "USB 3.1 Gen1" or "USB 3.2 Gen 1" or "SuperSpeed USB".